DC Pandey Solutions (JEE Main): First Law of Thermodynamics | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


Exercises 
For JEE Main 
  Subjective Questions 
  First Law of Thermodynamics 
Q 1.  In a certain chemical process, a lab technician supplies 254 J of heat to a system. At the same time, 
73 J of work are done on the system by its surroundings. What is the increase in the internal 
energy of the system? 
Q 2.  One mole of an ideal monoatomic gas is initially at 300 K. Find the final temperature if 200 J of 
heat are added as follows : 
  (a) at constant volume, (b) at constant pressure. 
Q 3.  Show how internal energy U varies with T in isochoric, isobaric and adiabatic process? 
Q 4.  A closed vessel 10 L in volume contains a diatomic gas under a pressure of 10
5
 N/ m
2
. What 
amount of heat should be imparted to the gas to increase the pressure in the vessel five times ? 
Q 5.  A diatomic ideal gas is heated at constant volume until its pressure becomes three times. It is again 
heated at constant pressure until its volume is doubled. Find the molar heat capacity for the whole 
process. 
Q 6.  Two moles of a certain gas at a temperature T0 = 300 K were cooled isochorically so that the 
pressure of the gas got reduced 2 times. Then as a result of isobaric process, the gas is allowed to 
expand till its temperature got back to the initial value. Find the total amount of heat absorbed by 
gas in this process. 
Q 7.  Five moles of an ideal monoatomic gas with an initial temperature of 127° C expand and in the 
process absorb 1200 J of heat and do 2100 J of work . What is the final temperature of the gas ? 
Q 8.  An ideal gas expands while the pressure is kept constant. During this process, does heat flow into 
the gas or out of the gas? Justify your answer. 
Q 9.  Find the change in the internal energy of 2 kg of water as it is heated from 0° C to 4° C. The 
specific heat capacity of water is 4200J/kg –K and its densities at 0° C and 4°C are 999.9 kg/m
3
 
and 1000 kg/m
3 
respectively. Atmospheric pressure = 10
5
 Pa. 
Q 10.  Calculate the increase in the internal energy of 10 g of water when it is heated from 0° C to 100° C 
and converted into steam at 100 kPa. The density of steam = 0.6 kg/m
3
. Specific heat capacity of 
water = 4200 J/kg-° Cand the latent heat of vaporization of water = 2.5 × 10
6
J/kg. 
Q 11.  One gram of water (1 cm
3
) becomes 1671cm of steam when boiled at a constant pressure of 1 atm 
(1.013 × 10
5
 Pa). The heat of vaporization at this pressure is Lv = 2.256 × 10
6 
J/kg. Compute (a) 
the work done by the water when it vaporizes and (b) its increase in internal energy.
 
Q 12.  A gas in a cylinder is held at a constant pressure of 2.30 × 10
5
 Pa and is cooled and compressed 
from 1.70 m
3
 to 1.20 m
3
. The internal energy of the gas decreases by 1.40 × 10
5
 J. (a) Find the 
work done by the gas. (b) Find the absolute value | Q | of the heat flow into or out of the gas and 
state the direction of the heat flow. (c) Does it matter whether or not the gas is ideal ? Why or why 
not? 
  Cyclic Process and Efficiency of Cycle 
Q 13.  An ideal gas is taken through a cyclic thermodynamic process through four steps. The amounts of 
heat involved in these steps are Q1 =5960J, Q2 =-5585J,Q3 = -2980J and Q4 = 3645 J respectively. 
Page 2


Exercises 
For JEE Main 
  Subjective Questions 
  First Law of Thermodynamics 
Q 1.  In a certain chemical process, a lab technician supplies 254 J of heat to a system. At the same time, 
73 J of work are done on the system by its surroundings. What is the increase in the internal 
energy of the system? 
Q 2.  One mole of an ideal monoatomic gas is initially at 300 K. Find the final temperature if 200 J of 
heat are added as follows : 
  (a) at constant volume, (b) at constant pressure. 
Q 3.  Show how internal energy U varies with T in isochoric, isobaric and adiabatic process? 
Q 4.  A closed vessel 10 L in volume contains a diatomic gas under a pressure of 10
5
 N/ m
2
. What 
amount of heat should be imparted to the gas to increase the pressure in the vessel five times ? 
Q 5.  A diatomic ideal gas is heated at constant volume until its pressure becomes three times. It is again 
heated at constant pressure until its volume is doubled. Find the molar heat capacity for the whole 
process. 
Q 6.  Two moles of a certain gas at a temperature T0 = 300 K were cooled isochorically so that the 
pressure of the gas got reduced 2 times. Then as a result of isobaric process, the gas is allowed to 
expand till its temperature got back to the initial value. Find the total amount of heat absorbed by 
gas in this process. 
Q 7.  Five moles of an ideal monoatomic gas with an initial temperature of 127° C expand and in the 
process absorb 1200 J of heat and do 2100 J of work . What is the final temperature of the gas ? 
Q 8.  An ideal gas expands while the pressure is kept constant. During this process, does heat flow into 
the gas or out of the gas? Justify your answer. 
Q 9.  Find the change in the internal energy of 2 kg of water as it is heated from 0° C to 4° C. The 
specific heat capacity of water is 4200J/kg –K and its densities at 0° C and 4°C are 999.9 kg/m
3
 
and 1000 kg/m
3 
respectively. Atmospheric pressure = 10
5
 Pa. 
Q 10.  Calculate the increase in the internal energy of 10 g of water when it is heated from 0° C to 100° C 
and converted into steam at 100 kPa. The density of steam = 0.6 kg/m
3
. Specific heat capacity of 
water = 4200 J/kg-° Cand the latent heat of vaporization of water = 2.5 × 10
6
J/kg. 
Q 11.  One gram of water (1 cm
3
) becomes 1671cm of steam when boiled at a constant pressure of 1 atm 
(1.013 × 10
5
 Pa). The heat of vaporization at this pressure is Lv = 2.256 × 10
6 
J/kg. Compute (a) 
the work done by the water when it vaporizes and (b) its increase in internal energy.
 
Q 12.  A gas in a cylinder is held at a constant pressure of 2.30 × 10
5
 Pa and is cooled and compressed 
from 1.70 m
3
 to 1.20 m
3
. The internal energy of the gas decreases by 1.40 × 10
5
 J. (a) Find the 
work done by the gas. (b) Find the absolute value | Q | of the heat flow into or out of the gas and 
state the direction of the heat flow. (c) Does it matter whether or not the gas is ideal ? Why or why 
not? 
  Cyclic Process and Efficiency of Cycle 
Q 13.  An ideal gas is taken through a cyclic thermodynamic process through four steps. The amounts of 
heat involved in these steps are Q1 =5960J, Q2 =-5585J,Q3 = -2980J and Q4 = 3645 J respectively. 
The corresponding quantities of work involved are W 1 =2200 J, W 2 =-825J, W 3 = - 1100 J and W4 
respectively. 
  (a) Find the value of W4 .  (b) What is the efficiency of the cycle ?  
Q 14.  One mole of an ideal monoatomic gas is taken round the cyclic process ABCA as shown in figure. 
Calculate: 
 
  (a) The work done by the gas. 
  (b) The heat rejected by the gas in the path CA and heat absorbed in the path AB. 
  (c) The net heat absorbed by the gas in the path BC. 
  (d) The maximum temperature attained by the gas during the cycle. 
Q 15.  Two moles of helium gas undergo a cyclic process as shown in figure. Assuming the gas to be 
ideal, calculate the following quantities in this process. 
 
  (a) The net change in the heat energy.  (b) The net work done. 
  (c) The net change in internal energy. 
Q 16.  n moles of a monoatomic gas are taken around in a cyclic process consisting of four processes 
along ABCDA as shown. All the lines on the P-V diagram have slope of magnitude Po / Vo . The 
pressure at A and C is P0 and the volumes at A and C are V0/2 and 3V0/2 respectively . Calculate 
the percentage efficiency of the cycle. 
 
Q 17.  A system is taken around the cycle shown in figure from state a to state b and then back to state a. 
The absolute value of the heat transfer during one cycle is 7200 J. (a) Does the system absorb or 
liberate heat when it goes around the cycle in the direction shown in the figure ? (b) What is the 
work W done by the system in one cycle ? (c) If the system goes around the cycle in a counter-
clock wise direction, does it absorb or liberate heat in one cycle? What is the magnitude of the 
heat absorbed or liberated in one counterclockwise cycle ? 
Page 3


Exercises 
For JEE Main 
  Subjective Questions 
  First Law of Thermodynamics 
Q 1.  In a certain chemical process, a lab technician supplies 254 J of heat to a system. At the same time, 
73 J of work are done on the system by its surroundings. What is the increase in the internal 
energy of the system? 
Q 2.  One mole of an ideal monoatomic gas is initially at 300 K. Find the final temperature if 200 J of 
heat are added as follows : 
  (a) at constant volume, (b) at constant pressure. 
Q 3.  Show how internal energy U varies with T in isochoric, isobaric and adiabatic process? 
Q 4.  A closed vessel 10 L in volume contains a diatomic gas under a pressure of 10
5
 N/ m
2
. What 
amount of heat should be imparted to the gas to increase the pressure in the vessel five times ? 
Q 5.  A diatomic ideal gas is heated at constant volume until its pressure becomes three times. It is again 
heated at constant pressure until its volume is doubled. Find the molar heat capacity for the whole 
process. 
Q 6.  Two moles of a certain gas at a temperature T0 = 300 K were cooled isochorically so that the 
pressure of the gas got reduced 2 times. Then as a result of isobaric process, the gas is allowed to 
expand till its temperature got back to the initial value. Find the total amount of heat absorbed by 
gas in this process. 
Q 7.  Five moles of an ideal monoatomic gas with an initial temperature of 127° C expand and in the 
process absorb 1200 J of heat and do 2100 J of work . What is the final temperature of the gas ? 
Q 8.  An ideal gas expands while the pressure is kept constant. During this process, does heat flow into 
the gas or out of the gas? Justify your answer. 
Q 9.  Find the change in the internal energy of 2 kg of water as it is heated from 0° C to 4° C. The 
specific heat capacity of water is 4200J/kg –K and its densities at 0° C and 4°C are 999.9 kg/m
3
 
and 1000 kg/m
3 
respectively. Atmospheric pressure = 10
5
 Pa. 
Q 10.  Calculate the increase in the internal energy of 10 g of water when it is heated from 0° C to 100° C 
and converted into steam at 100 kPa. The density of steam = 0.6 kg/m
3
. Specific heat capacity of 
water = 4200 J/kg-° Cand the latent heat of vaporization of water = 2.5 × 10
6
J/kg. 
Q 11.  One gram of water (1 cm
3
) becomes 1671cm of steam when boiled at a constant pressure of 1 atm 
(1.013 × 10
5
 Pa). The heat of vaporization at this pressure is Lv = 2.256 × 10
6 
J/kg. Compute (a) 
the work done by the water when it vaporizes and (b) its increase in internal energy.
 
Q 12.  A gas in a cylinder is held at a constant pressure of 2.30 × 10
5
 Pa and is cooled and compressed 
from 1.70 m
3
 to 1.20 m
3
. The internal energy of the gas decreases by 1.40 × 10
5
 J. (a) Find the 
work done by the gas. (b) Find the absolute value | Q | of the heat flow into or out of the gas and 
state the direction of the heat flow. (c) Does it matter whether or not the gas is ideal ? Why or why 
not? 
  Cyclic Process and Efficiency of Cycle 
Q 13.  An ideal gas is taken through a cyclic thermodynamic process through four steps. The amounts of 
heat involved in these steps are Q1 =5960J, Q2 =-5585J,Q3 = -2980J and Q4 = 3645 J respectively. 
The corresponding quantities of work involved are W 1 =2200 J, W 2 =-825J, W 3 = - 1100 J and W4 
respectively. 
  (a) Find the value of W4 .  (b) What is the efficiency of the cycle ?  
Q 14.  One mole of an ideal monoatomic gas is taken round the cyclic process ABCA as shown in figure. 
Calculate: 
 
  (a) The work done by the gas. 
  (b) The heat rejected by the gas in the path CA and heat absorbed in the path AB. 
  (c) The net heat absorbed by the gas in the path BC. 
  (d) The maximum temperature attained by the gas during the cycle. 
Q 15.  Two moles of helium gas undergo a cyclic process as shown in figure. Assuming the gas to be 
ideal, calculate the following quantities in this process. 
 
  (a) The net change in the heat energy.  (b) The net work done. 
  (c) The net change in internal energy. 
Q 16.  n moles of a monoatomic gas are taken around in a cyclic process consisting of four processes 
along ABCDA as shown. All the lines on the P-V diagram have slope of magnitude Po / Vo . The 
pressure at A and C is P0 and the volumes at A and C are V0/2 and 3V0/2 respectively . Calculate 
the percentage efficiency of the cycle. 
 
Q 17.  A system is taken around the cycle shown in figure from state a to state b and then back to state a. 
The absolute value of the heat transfer during one cycle is 7200 J. (a) Does the system absorb or 
liberate heat when it goes around the cycle in the direction shown in the figure ? (b) What is the 
work W done by the system in one cycle ? (c) If the system goes around the cycle in a counter-
clock wise direction, does it absorb or liberate heat in one cycle? What is the magnitude of the 
heat absorbed or liberated in one counterclockwise cycle ? 
 
Q 18.  A thermodynamic system undergoes a cyclic process as shown in figure. The cycle consists of two 
closed loops, loop I and loop II.  
 
  (a) Over one complete cycle, does the system do positive or negative work ?  
  (b) In each of loops I and II, is the net work done by the system positive or negative ?  
  (c) Over one complete cycle, does heat flow into or out of the system ?  
  (d) In each of loops I and II, does heat flow into or out of the system ? 
Q 19.  1.0 k-mol of a sample of helium gas is put through the cycle of operations shown in figure. BC is 
an isothermal process and PA = 1.00 atm ,VA =22.4m
3
,PB =2.00 atm. What are TA, TB and VC ? 
 
Q 20.  For the thermodynamic cycle shown in figure find  
  (a) net output work of the gas during the cycle, (b) net heat flow into the gas per cycle. 
 
Q 21.  The density ( ?)
 
versus pressure (P) graph of an ideal gas (monoatomic) undergoing a cyclic 
process is shown in figure. The gas taken has molecular mass M and one mole of gas is taken. 
Page 4


Exercises 
For JEE Main 
  Subjective Questions 
  First Law of Thermodynamics 
Q 1.  In a certain chemical process, a lab technician supplies 254 J of heat to a system. At the same time, 
73 J of work are done on the system by its surroundings. What is the increase in the internal 
energy of the system? 
Q 2.  One mole of an ideal monoatomic gas is initially at 300 K. Find the final temperature if 200 J of 
heat are added as follows : 
  (a) at constant volume, (b) at constant pressure. 
Q 3.  Show how internal energy U varies with T in isochoric, isobaric and adiabatic process? 
Q 4.  A closed vessel 10 L in volume contains a diatomic gas under a pressure of 10
5
 N/ m
2
. What 
amount of heat should be imparted to the gas to increase the pressure in the vessel five times ? 
Q 5.  A diatomic ideal gas is heated at constant volume until its pressure becomes three times. It is again 
heated at constant pressure until its volume is doubled. Find the molar heat capacity for the whole 
process. 
Q 6.  Two moles of a certain gas at a temperature T0 = 300 K were cooled isochorically so that the 
pressure of the gas got reduced 2 times. Then as a result of isobaric process, the gas is allowed to 
expand till its temperature got back to the initial value. Find the total amount of heat absorbed by 
gas in this process. 
Q 7.  Five moles of an ideal monoatomic gas with an initial temperature of 127° C expand and in the 
process absorb 1200 J of heat and do 2100 J of work . What is the final temperature of the gas ? 
Q 8.  An ideal gas expands while the pressure is kept constant. During this process, does heat flow into 
the gas or out of the gas? Justify your answer. 
Q 9.  Find the change in the internal energy of 2 kg of water as it is heated from 0° C to 4° C. The 
specific heat capacity of water is 4200J/kg –K and its densities at 0° C and 4°C are 999.9 kg/m
3
 
and 1000 kg/m
3 
respectively. Atmospheric pressure = 10
5
 Pa. 
Q 10.  Calculate the increase in the internal energy of 10 g of water when it is heated from 0° C to 100° C 
and converted into steam at 100 kPa. The density of steam = 0.6 kg/m
3
. Specific heat capacity of 
water = 4200 J/kg-° Cand the latent heat of vaporization of water = 2.5 × 10
6
J/kg. 
Q 11.  One gram of water (1 cm
3
) becomes 1671cm of steam when boiled at a constant pressure of 1 atm 
(1.013 × 10
5
 Pa). The heat of vaporization at this pressure is Lv = 2.256 × 10
6 
J/kg. Compute (a) 
the work done by the water when it vaporizes and (b) its increase in internal energy.
 
Q 12.  A gas in a cylinder is held at a constant pressure of 2.30 × 10
5
 Pa and is cooled and compressed 
from 1.70 m
3
 to 1.20 m
3
. The internal energy of the gas decreases by 1.40 × 10
5
 J. (a) Find the 
work done by the gas. (b) Find the absolute value | Q | of the heat flow into or out of the gas and 
state the direction of the heat flow. (c) Does it matter whether or not the gas is ideal ? Why or why 
not? 
  Cyclic Process and Efficiency of Cycle 
Q 13.  An ideal gas is taken through a cyclic thermodynamic process through four steps. The amounts of 
heat involved in these steps are Q1 =5960J, Q2 =-5585J,Q3 = -2980J and Q4 = 3645 J respectively. 
The corresponding quantities of work involved are W 1 =2200 J, W 2 =-825J, W 3 = - 1100 J and W4 
respectively. 
  (a) Find the value of W4 .  (b) What is the efficiency of the cycle ?  
Q 14.  One mole of an ideal monoatomic gas is taken round the cyclic process ABCA as shown in figure. 
Calculate: 
 
  (a) The work done by the gas. 
  (b) The heat rejected by the gas in the path CA and heat absorbed in the path AB. 
  (c) The net heat absorbed by the gas in the path BC. 
  (d) The maximum temperature attained by the gas during the cycle. 
Q 15.  Two moles of helium gas undergo a cyclic process as shown in figure. Assuming the gas to be 
ideal, calculate the following quantities in this process. 
 
  (a) The net change in the heat energy.  (b) The net work done. 
  (c) The net change in internal energy. 
Q 16.  n moles of a monoatomic gas are taken around in a cyclic process consisting of four processes 
along ABCDA as shown. All the lines on the P-V diagram have slope of magnitude Po / Vo . The 
pressure at A and C is P0 and the volumes at A and C are V0/2 and 3V0/2 respectively . Calculate 
the percentage efficiency of the cycle. 
 
Q 17.  A system is taken around the cycle shown in figure from state a to state b and then back to state a. 
The absolute value of the heat transfer during one cycle is 7200 J. (a) Does the system absorb or 
liberate heat when it goes around the cycle in the direction shown in the figure ? (b) What is the 
work W done by the system in one cycle ? (c) If the system goes around the cycle in a counter-
clock wise direction, does it absorb or liberate heat in one cycle? What is the magnitude of the 
heat absorbed or liberated in one counterclockwise cycle ? 
 
Q 18.  A thermodynamic system undergoes a cyclic process as shown in figure. The cycle consists of two 
closed loops, loop I and loop II.  
 
  (a) Over one complete cycle, does the system do positive or negative work ?  
  (b) In each of loops I and II, is the net work done by the system positive or negative ?  
  (c) Over one complete cycle, does heat flow into or out of the system ?  
  (d) In each of loops I and II, does heat flow into or out of the system ? 
Q 19.  1.0 k-mol of a sample of helium gas is put through the cycle of operations shown in figure. BC is 
an isothermal process and PA = 1.00 atm ,VA =22.4m
3
,PB =2.00 atm. What are TA, TB and VC ? 
 
Q 20.  For the thermodynamic cycle shown in figure find  
  (a) net output work of the gas during the cycle, (b) net heat flow into the gas per cycle. 
 
Q 21.  The density ( ?)
 
versus pressure (P) graph of an ideal gas (monoatomic) undergoing a cyclic 
process is shown in figure. The gas taken has molecular mass M and one mole of gas is taken. 
 
  (a) Find work done in each process.  
  (b) Find heat rejected by gas in one complete cycle. 
  (c) Find the efficiency of the cycle. 
Q 22.  An ideal gas goes through the cycle abc. For the complete cycle 800 J of heat flows out of the gas. 
Process ab is at constant pressure and process bc is at constant volume . In process c-a, P ? V. 
States a and b have temperatures Ta = 200 K and Tb = 300 K.  
  (a) Sketch the P-V diagram for the cycle, (b) What is the work W for the process ca ? 
Q 23.  A monoatomic gas is expanded adiabatically from volume V0 to 2 V 0 and then is brought back to 
the initial state through an isothermal and isochoric process respectively. Plot the P-V diagram of 
the complete cycle and find the efficiency of the cycle. 
Solutions 
1. ?U = Q - W 
   = 254 -(-73)= 327 J 
2.  (a) 
  ?   200 =1.5 × 8.31(T f - 300)  
  Solving we get, 
   Tf = 316K 
  (b) 
  ?   200 = 2.5 × 8.31(Tf - 300) 
   
3.  For all process, 
   
4.  V = constant 
  From   PV = nRT 
   
    
5.  First process 
   V = constant 
   
Page 5


Exercises 
For JEE Main 
  Subjective Questions 
  First Law of Thermodynamics 
Q 1.  In a certain chemical process, a lab technician supplies 254 J of heat to a system. At the same time, 
73 J of work are done on the system by its surroundings. What is the increase in the internal 
energy of the system? 
Q 2.  One mole of an ideal monoatomic gas is initially at 300 K. Find the final temperature if 200 J of 
heat are added as follows : 
  (a) at constant volume, (b) at constant pressure. 
Q 3.  Show how internal energy U varies with T in isochoric, isobaric and adiabatic process? 
Q 4.  A closed vessel 10 L in volume contains a diatomic gas under a pressure of 10
5
 N/ m
2
. What 
amount of heat should be imparted to the gas to increase the pressure in the vessel five times ? 
Q 5.  A diatomic ideal gas is heated at constant volume until its pressure becomes three times. It is again 
heated at constant pressure until its volume is doubled. Find the molar heat capacity for the whole 
process. 
Q 6.  Two moles of a certain gas at a temperature T0 = 300 K were cooled isochorically so that the 
pressure of the gas got reduced 2 times. Then as a result of isobaric process, the gas is allowed to 
expand till its temperature got back to the initial value. Find the total amount of heat absorbed by 
gas in this process. 
Q 7.  Five moles of an ideal monoatomic gas with an initial temperature of 127° C expand and in the 
process absorb 1200 J of heat and do 2100 J of work . What is the final temperature of the gas ? 
Q 8.  An ideal gas expands while the pressure is kept constant. During this process, does heat flow into 
the gas or out of the gas? Justify your answer. 
Q 9.  Find the change in the internal energy of 2 kg of water as it is heated from 0° C to 4° C. The 
specific heat capacity of water is 4200J/kg –K and its densities at 0° C and 4°C are 999.9 kg/m
3
 
and 1000 kg/m
3 
respectively. Atmospheric pressure = 10
5
 Pa. 
Q 10.  Calculate the increase in the internal energy of 10 g of water when it is heated from 0° C to 100° C 
and converted into steam at 100 kPa. The density of steam = 0.6 kg/m
3
. Specific heat capacity of 
water = 4200 J/kg-° Cand the latent heat of vaporization of water = 2.5 × 10
6
J/kg. 
Q 11.  One gram of water (1 cm
3
) becomes 1671cm of steam when boiled at a constant pressure of 1 atm 
(1.013 × 10
5
 Pa). The heat of vaporization at this pressure is Lv = 2.256 × 10
6 
J/kg. Compute (a) 
the work done by the water when it vaporizes and (b) its increase in internal energy.
 
Q 12.  A gas in a cylinder is held at a constant pressure of 2.30 × 10
5
 Pa and is cooled and compressed 
from 1.70 m
3
 to 1.20 m
3
. The internal energy of the gas decreases by 1.40 × 10
5
 J. (a) Find the 
work done by the gas. (b) Find the absolute value | Q | of the heat flow into or out of the gas and 
state the direction of the heat flow. (c) Does it matter whether or not the gas is ideal ? Why or why 
not? 
  Cyclic Process and Efficiency of Cycle 
Q 13.  An ideal gas is taken through a cyclic thermodynamic process through four steps. The amounts of 
heat involved in these steps are Q1 =5960J, Q2 =-5585J,Q3 = -2980J and Q4 = 3645 J respectively. 
The corresponding quantities of work involved are W 1 =2200 J, W 2 =-825J, W 3 = - 1100 J and W4 
respectively. 
  (a) Find the value of W4 .  (b) What is the efficiency of the cycle ?  
Q 14.  One mole of an ideal monoatomic gas is taken round the cyclic process ABCA as shown in figure. 
Calculate: 
 
  (a) The work done by the gas. 
  (b) The heat rejected by the gas in the path CA and heat absorbed in the path AB. 
  (c) The net heat absorbed by the gas in the path BC. 
  (d) The maximum temperature attained by the gas during the cycle. 
Q 15.  Two moles of helium gas undergo a cyclic process as shown in figure. Assuming the gas to be 
ideal, calculate the following quantities in this process. 
 
  (a) The net change in the heat energy.  (b) The net work done. 
  (c) The net change in internal energy. 
Q 16.  n moles of a monoatomic gas are taken around in a cyclic process consisting of four processes 
along ABCDA as shown. All the lines on the P-V diagram have slope of magnitude Po / Vo . The 
pressure at A and C is P0 and the volumes at A and C are V0/2 and 3V0/2 respectively . Calculate 
the percentage efficiency of the cycle. 
 
Q 17.  A system is taken around the cycle shown in figure from state a to state b and then back to state a. 
The absolute value of the heat transfer during one cycle is 7200 J. (a) Does the system absorb or 
liberate heat when it goes around the cycle in the direction shown in the figure ? (b) What is the 
work W done by the system in one cycle ? (c) If the system goes around the cycle in a counter-
clock wise direction, does it absorb or liberate heat in one cycle? What is the magnitude of the 
heat absorbed or liberated in one counterclockwise cycle ? 
 
Q 18.  A thermodynamic system undergoes a cyclic process as shown in figure. The cycle consists of two 
closed loops, loop I and loop II.  
 
  (a) Over one complete cycle, does the system do positive or negative work ?  
  (b) In each of loops I and II, is the net work done by the system positive or negative ?  
  (c) Over one complete cycle, does heat flow into or out of the system ?  
  (d) In each of loops I and II, does heat flow into or out of the system ? 
Q 19.  1.0 k-mol of a sample of helium gas is put through the cycle of operations shown in figure. BC is 
an isothermal process and PA = 1.00 atm ,VA =22.4m
3
,PB =2.00 atm. What are TA, TB and VC ? 
 
Q 20.  For the thermodynamic cycle shown in figure find  
  (a) net output work of the gas during the cycle, (b) net heat flow into the gas per cycle. 
 
Q 21.  The density ( ?)
 
versus pressure (P) graph of an ideal gas (monoatomic) undergoing a cyclic 
process is shown in figure. The gas taken has molecular mass M and one mole of gas is taken. 
 
  (a) Find work done in each process.  
  (b) Find heat rejected by gas in one complete cycle. 
  (c) Find the efficiency of the cycle. 
Q 22.  An ideal gas goes through the cycle abc. For the complete cycle 800 J of heat flows out of the gas. 
Process ab is at constant pressure and process bc is at constant volume . In process c-a, P ? V. 
States a and b have temperatures Ta = 200 K and Tb = 300 K.  
  (a) Sketch the P-V diagram for the cycle, (b) What is the work W for the process ca ? 
Q 23.  A monoatomic gas is expanded adiabatically from volume V0 to 2 V 0 and then is brought back to 
the initial state through an isothermal and isochoric process respectively. Plot the P-V diagram of 
the complete cycle and find the efficiency of the cycle. 
Solutions 
1. ?U = Q - W 
   = 254 -(-73)= 327 J 
2.  (a) 
  ?   200 =1.5 × 8.31(T f - 300)  
  Solving we get, 
   Tf = 316K 
  (b) 
  ?   200 = 2.5 × 8.31(Tf - 300) 
   
3.  For all process, 
   
4.  V = constant 
  From   PV = nRT 
   
    
5.  First process 
   V = constant 
   
  Pressure becomes three times. 
  Therefore temperature also becomes three times. 
    (Tf = 3Ti) 
  Second process 
   P = constant 
   
  Volume is doubled. So temperature also becomes two time.  
   (T'f = 6Ti) 
   
    
6.  First Process  
   V = constant 
   
  Pressure becomes half. So, temperature also becomes half. 
    
   = - 300 C V  
  Second Process 
   P = constant 
    
   = 2CP(300-150) = 300 CP 
   Q = Q1 + Q2 
   = 300(CP - CV) = 300 R 
   = 300 × 8.31 = 2493 J 
7.  
   
   Tf = 385 K 
    
8.  P = constant 
   
  As the gas expands V increases. So, T also increases. Hence is positive. Therefore in the 
expression, 
    
  Q is positive. 
9.