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Mechanical Engineering Exam  >  Mechanical Engineering Notes  >  Thermodynamics  >  GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions

GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering PDF Download

Q1: A heat pump (H.P.) is driven by the work output a heat engine (H.E.) as shown in the figure. The heat engine extracts  150kJ of heat from the source at 1000k. The heat pump absorbs heat from the ambient at  280K  and delivers heat to the room which is maintained at 300k Considering the combined system to be ideal, the total amount of heat delivered to the room together by the heat engine and heat pump is ____ kJ (answer in integer).       (2024)
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
(a) 1254
(b) 2358
(c) 1620
(d) 1456
Ans:(d)
Sol:

GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
or,
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
So, net heat delivered to room
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

Q2:   A piston-cylinder arrangement shown in the figure has a stop located  2 m above the base. The cylinder initially contains air at
140 kPa  and 350 o C  and the piston is resting in equilibrium at a position which is 1m above the stops. The system is now cooled to  the    ambient temperature  of 25oC  Consider air to be an ideal gas with a value of gas constant R=0.287 kJ (kg.K)  The absolute value of           specific work done during the process is _______ kJ/kg (rounded off to 1 decimal place).       (2024)
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
(a) 59.6
(b) 63.2
(c) 47.5
(d) 88.6
Ans:(a)

Sol:

GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
For constant pressure process
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

[as the stopper, length is 2 m area is constant]
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

 Q3:  Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is massless and cross-sectional area of the cylinder is A. The fluid inside the cylinder is air (considered as a perfect gas), with 𝛾  being the ratio of the specific heat at constant pressure to the specific heat at constant volume for air. The piston is initially located at a position L 1 The initial pressure of the air inside the cylinder is P1 ≫ P0 , where P0  is the atmospheric pressure. The stop S1 is instantaneously removed and the piston moves to the position  L2   where the equilibrium pressure of air inside the cylinder isP2  ≫ P0       (2023) 
What is the work done by the piston on the atmosphere during this process?
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
(a) 0
(b) P0 A(L2 - L1 ) 

(c) GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
(d) GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
Ans :(b)

Sol: 
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
Initial volume V 1 = L1 × A  
Final volume 𝑉 2 = 𝐿 2 × 𝐴    
Work done by atmospheric air=GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

Q4: A heat engine extracts heat (QH)  from a thermal reservoir at a temperature of  1000K and rejects heat(QL)

 to a thermal reservoir at a temperature of 100K, while producing work  (W). Which one of the combinations of

(QH ,QL,W)   given is allowed?      (2023)
(a) QH=2000J,QL=500J,W=1000J
(b) 𝑄𝐻=2000𝐽,𝑄𝐿=750𝐽,𝑊=1250𝐽
 (c) 𝑄𝐻=6000𝐽,𝑄𝐿=500𝐽,𝑊=5500𝐽

  (d) QH=6000J,QL=600J,W=5500J
Ans:(b)
Sol: For a reversible engine, the rate of heat rejection is minimum.
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
For process to be feasible
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
 for option GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
So cyclic process is possible.

Q5: Consider 1 kg of an ideal gas at 1 bar and 300 K contained in a rigid and perfectly insulated container. The specific heat of the gas at constant volume cv  is equal to  750 Jkg -1K-1 . A stirrer performs  255 kj  of work on the gas. Assume that the container does not participate in the thermodynamic interaction. The final pressure of the gas will be ______ bar (in integer).      (2022Set 2)
(a) 1

(b) 2

(c) 3
(d) 4 

Ans: (b)
Sol: m=1kg,P1=1bar,T1=300K
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

V=Constant

Wexpansion =0
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
Using Ist law of thermodynamics
Q-W =dU =mcv (T2 -T1)
0-(-255) =1×0.75(T2−300)

T2 =600k
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

Q6: A polytropic process is carried out from an initial pressure of 110 kPa and volume of 5m3  to a final volume of 2.5m3. The polytropic  index is given by n = 1.2. The absolute value of the work done during the process is _______ kJ (round off to 2 decimal places).      (2022 Set 1)
(a) 408.92
(b) 215.58
(c) 852.36
(d) 789. 14
Ans(a)

Sol: Polytropic process]
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

Q7: In a steam power plant, superheated steam at 10 MPa and 5000C.  is expanded isentropically in a turbine until it becomes a saturated vapour. It is then reheated at constant pressure to  5000C.  The steam is next expanded isentropically in another turbine until it reaches the condenser pressure of 20 kPa. Relevant properties of steam are given in the following two tables. The work done by both the turbines together is ______ kJ/kg (roundoff to the nearest integer).      (2020Set 2)
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

(a) 1513

(b) 1245

(c) 832

(d) 1825
Ans: (a)

Sol: 
Given data: GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

Q8: Moist air at 105 kPa, 300 C and 80% relative humidity flows over a cooling coil in an insulated air-conditioning duct. Saturated air exits the duct at 100 kPa  and 150C The saturation pressure of water at 300 C and150C are 4.24 kPa and 1.7 kPa   respectively.  Molecular weight of water is 18 g/mol and that of air is28.94 g/mol .The mass of water condensing out from the duct is ______ g/kg of dry air (round off to 2 decimal places).      (2020 Set2) 

(a) 8.21

(b) 15.24

(c) 10.01

(d) 12.24 

Ans(c)

Sol: 
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

Q9: Air is contained in a frictionless piston-cylinder arrangement as shown in the figure.
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
The atmospheric pressure is 100 kPa and the initial pressure of air in the cylinder is 105 kPa. The area of piston is 300cm2. Heat is now added and the piston moves slowly from its initial position until it reaches the stops  The spring constant of the linear spring is 12.5 N/mm  Considering the air inside the cylinder as the system, the work interaction is ________ J. (round off to the nearest integer)
    (2020Set2)
(a) 1

(b) 544

(c) 254

(d) 623

Ans: (b)
Sol:  
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
1-2 constant pressure
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
Alternate Solution:

Total work = Workdone because of 105 kPa pressure + Workdone against spring which is equal to energy stored in spring
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

Q10: One kg of air, initially at a temperature of  127OC , expands reversibly at a constant pressure until the volume is doubled. If the gas constant of air 287 J/kg .K  the magnitude of work transfer is __________ kJ (round off to 2 decimal      (2020Set1) 

(a) 156.6
(b) 114.8

(c) 89.8
(d) 124.4
Ans: (b) 

Sol:
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
                                             GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering
GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:A gas is heated in a duct as it flows over a resistance heater. Consider a 101 kW electric heating system. The gas enters the heating section of the duct at 100 kPa and 27°C with a volume flow rate of 15 m3/s. If heat is lost from the gas in the duct to the surroundings at a rate of 51 kW, the exit temperature of the gas is (Assume constant pressure, ideal gas, negligible change in kinetic and potential energies and constant specific heat : Cp = 1 kJ/kg. K; R = 0.5 kJ/kg K).

[2019 , Set 1]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:A calorically perfect gas (specific heat at constant pressure 1000 J/kgK) enters and leaves a gas turbine with the same velocity.The emperature of the gas at turbine entry and exit are 1100 K and 400 K, respectively. The power produced is 4.6 MW and heat escapes at the rate of 300 kJ/s through the turbine casing.The mass flow rate of the gas (in kg/s) through the turbine is

[2017, Set-2]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:A compressor undergoes a reversible, steady flow process. The gas at inlet and outlet of the compressor is designated as state 1 and state 2 respectively. Potential and kinetic energy changes are to be ignored. The following notations are used: v = specific volume and P = pressure of the gas. The specific work required to be supplied to the compressor for this gas compression process is

[2009]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:In a steady state steady flow process taking place in a device with a single inlet and a single outlet, the work done per unit mass flow rate is given by GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineeringwhere v is the specific volume and p is the pressure, The expression for w given above

[2008]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:A rigid, insulated tank is initially evacuated.
The tank is connected with a supply line through which air (assumed to be ideal gas with constant specific heats) passes at 1 MPa, 350°C.

GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions | Thermodynamics - Mechanical Engineering

A valve connected with the supply line is opened and the tank is charged with air until the final pressure inside the tank reaches 1 MPa. The final temperature inside the tank

[2008]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:A small steam whistle (perfectly insulated and doing no shaft work) causes a drop of 0.8 kJ/kg in enthalpy of steam from entry to exit. If the kinetic energy of the steam at entry is negligible, the velocity of the steam at exit is

[2001]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:When an ideal gas with constant specific heats is throttled adiabatically, with negligible changes in kinetic and potential energies.

[2000]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:A steam turbine receives steam steadily at 10 bar with a enthalpy of 3000 kJ/kg and discharges at 1 bar with an enthalpy of 2700 kJ/kg. The work output is 250 kJ/kg. The changes in kinetic and potential energies are negligible. The heat transfer from the turbine casing to the surroundings is equal to

[2000]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:For reversible a diabatic compression in a steady flow process, the work transfer per unit mass is

[1996]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:The contents of a well-insulated tank are heated by a resistor of 23 W in which 10 A current is flowing. Consider the tank along with its contents as a thermodynamic system. The work done by the system and the heat transfer to the system are positive. The rates of heat (Q), work (W) and change in internal energy (ΔU) during the process (kW) are

[2011]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:A gas expands in a frictionless piston-cylinder arrangement. The expansion process is very slow, and is resisted by an ambient pressure of 100 kPa. During the expansion process, the pressure of the system (gas) remains constant at 300 kPa. The change in volume of the gas is 0.01 m3. The maximum amount of work that could be utilized from the above process is.

[2008]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:Which of the following relationships is valid only for reversible processes undergone by a closed system of simple compressible substance (neglect changes in kinetic and potential energy)?

[2007]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:Gauge pressure of air to which the ball must have been originally inflated so that it would be equal 1 bar gauge at the stadium is

[2006]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:The amount of heat lost by the air in the football and the gauge pressure of air in the football at the stadium respectively equal

[2006]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:A 2 kW, 40 litres water heater is switched on for 20 minutes. The heat capacity cp for water is 4.2 kJ/kgK. Assuming all the electrical energy has gone into heating the water, increase of the water temperature in degree centigrade is

[2003]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:The first law of thermodynamics takes the form W = –ΔH when applied to

[1993]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:The internal energy of an ideal gas is a function of

[2016 , Set-2]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:For an ideal gas with constant values of specific heats, for calculation of the specific enthalpy,

[2015, Set-1]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:A frictionless piston-cylinder device contains a gas initially at 0.8 MPa and 0.015 m3. It expands quasistatically at constant temperature to a final volume of 0.030 m3. The work output (in kJ) during this process will be

[2009]

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Question for GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions
Try yourself:A balloon containing an ideal gas is initially kept in an evacuated and insulated room. The balloon ruptures and the gas fills up the entire room. Which one of the following statements is TRUE at the end of above process?

[2008]

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FAQs on GATE Past Year Questions: First Law Of Thermodynamics, Heat, Work And Energy Interactions - Thermodynamics - Mechanical Engineering

1. What is the first law of thermodynamics?
Ans. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another.
2. How is heat related to the first law of thermodynamics?
Ans. Heat is a form of energy that can be transferred into or out of a system during a thermodynamic process, in accordance with the first law of thermodynamics.
3. Can you explain the concept of work in the context of the first law of thermodynamics?
Ans. Work is the transfer of energy that occurs when a force is applied over a distance. In the context of the first law of thermodynamics, work can be used to change the internal energy of a system.
4. How do heat and work interactions play a role in the first law of thermodynamics?
Ans. Heat and work interactions are essential in understanding how energy is transferred within a system and how it affects the system's internal energy, as described by the first law of thermodynamics.
5. What are some real-world applications of the first law of thermodynamics?
Ans. The first law of thermodynamics is used in various applications, such as analyzing heat engines, refrigeration systems, and chemical reactions, to understand and predict energy transfers and conversions.
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