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Which statement is incorrect?
All reversible engines working for the same temperature of source and sink have same efficiencies. If the temperatures are different, the efficiency is different.
Heat given to a body which raises its temperature by 1°C is
Heat required for raising the temperature of the whole body by 1ºC is called the thermal capacity of the body.
Infrared radiation is detected by
Pyrometer is used to detect infrared radiation.
Which of the following is more close to a black body?
Black board paint is quite approximately equal to black bodies.
Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will
Since pressure and volume are not changing, so temperature remains same.
If massenergy equivalence is taken into account, when water is cooled to form ice, the mass of water should
When water is cooled to form ice, energy is released from water in the form of heat. As energy is equivalent to mass therefore when water is cooled to ice, its mass decreases.
At what temperature is the r.m.s velocity of a hydrogen molecule equal to that of an oxygen molecule at 47°C?
Even Carnot engine cannot give 100% efficiency because we cannot
The temperature of 0 K (absolute zero) can not be obtained .
1 mole of a gas with γ = 7/5 is mixed with 1 mole of a gas with γ = 5/3, then the value of g for the resulting mixture is
For mixture of gases
Two spheres of the same material have radii 1 m and 4 m and temperatures 4000 K and 2000 K respectively. The ratio of the energy radiated per second by the first sphere to that by the second is
The energy radiated per second is given by
For same material e is same. σ is stefan's constant
“Heat cannot by itself flow from a body at lower temperature to a body at higher temperature” is a statement or consequen ce of
This is a statement of second law of thermodynamics
During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature.
The ratio CP /CV for the gas is
But for an adiabatic process, the pressure temperature relationship is given by
Which of the following parameters does not characterize the thermodynamic state of matter?
Work is a path function. The remaining three parameters are state function.
A Carnot engine takes 3 *10 ^{6} cal. of heat from a reservoir at 627^{o} C , and gives it to a sink at 27^{ o} C . The work done by the engine is
The earth radiates in the infrared region of the spectrum. The spectrum is correctly given by
Wein’s law correctly explains the spectrum
According to Newton’s law of cooling, the rate of cooling of a body is proportional to ( Δθ)^{n} , wher e Δθ is the difference of the temperature of the body and the surroundings, and n is equal to
One mole of ideal monatomic gas ( γ = 5 / 3) is mixed with one mole of diatomic gas (γ = 7 / 5) . What is g for the mixture? γ Denotes the ratio of specific heat at constant pressure, to that at constant volume
If the temperature of the sun were to increase from T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on earth to what it was previously will be
Which of the following statements is correct for any thermodynamic system ?
Internal energy and entropy are state function, they do not depend upon path taken.
Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T_{1} ,T_{2} ), volume (V_{1 },V_{2}) and pressure ( P_{1} ,P_{2}) respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be
Here Q = 0 and W = 0. Therefore from first law of thermodynamics ΔU = Q + W = 0
∴ Internal energy of thesystem with partition = Internal energy of the system without partition.
The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively, are T_{2} and T_{1} (T_{2} >T_{1}) . The rate of heat transfer through the slab, in a steady state is with f equal to
The thermal resistance
Which of the following is incorrect regarding the first law of thermodynamics?
First law is applicable to a cyclic process. Concept of entropy is introduced by the second law.
The figure shows a system of two concentric spheres of radii r_{1} and r_{2} are kept at temperatures T_{1} and T_{2}, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to
Consider a shell of thickness (dr) and of radius (r) and the temperature of inner and outer surfaces of this shell be T, (T – dT)
A system goes from A to B via two processes I and II as shown in figure. If ΔU_{1} and ΔU_{2} are the changes in internal energies in the processes I and II respectively, then
Change in internal energy do not depend upon the path followed by the process. It only depends on initial and final states i.e., ΔU_{1} = ΔU_{2}
The temperatureentropy diagram of a reversible engine cycle is given in the figure. Its efficiency is
A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio C_{p}/C_{v } of the mixture is
Assuming the Sun to be a spherical body of radius R at a temperature of TK, evaluate the total radiant powerd incident of Earth at a distance r from the Sun
where r_{0} is the radius of the Earth and σ is Stefan's constant.
Total power radiated by Sun =
The intensity of power at earth's surface =
Total power received by Earth =
Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature T_{0}, while Box contains one mole of helium at temperature . The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases, T_{f} in terms of T_{0} is
Heat lost by He = Heat gained by N_{2}
_{}
The work of 146 kJ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by 7°C. The gas is (R = 8.3 J mol^{–1} K^{–1})
Hence the gas is diatomic.
When a system is taken from state i to state f along the path iaf, it is found that Q =50 cal and W = 20 cal. Along the path ibf Q = 36 cal. W along the path ibf is
For path iaf,
For path ibf
A Carnot engine, having an efficiency of η= 1/10 as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is
The efficiency (η) of a Carnot engine and the coefficient of performance (β) of a refrigerator are related as
Also, Coefficient of performance (β) is given by Q_{2}/W
β= , where Q_{2} is the energy absorbed from the reservoir.
One end of a thermally insulated rod is kept at a temperature T_{1} and the other at T_{2}. The rod is composed of two sections of length l_{1} and l_{2} and thermal conductivities K_{1} and K_{2} respectively. The temperature at the interface of the two section is
If C_{P} and C_{V} denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then
According to Mayer's relationship C_{P} – C_{V} = R
The speed of sound in oxygen (O_{2}) at a certain temperature is 460 ms^{–1}. The speed of sound in helium (He) at the same temperature will be (assume both gases to be ideal)
The speed of sound in a gas is given by
An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V_{1} and contains ideal gas at pressure P_{1} and temperature T_{1}. The other chamber has volume V, and contains ideal gas at pressure P_{2} and temperature T_{2}. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be
Same as A . 20
A long metallic bar is carrying heat from one of its ends to the other end under steady–state. The variation of temperature θ along the length x of the bar from its hot end is best described by which of the following figures?
The heat flow rate is given by
where θ1 is the temperature of hot end and v is temperature at a distance x from hot end.
The above equation can be graphically represented by option (a) .
Two moles of helium gas are taken over the cycle ABCDA, as shown in the PT diagram.
Q.37. Assuming the gas to be ideal the work done on the gas in taking it from A to B is :
A to B is an isobaric process. The work done
W = nR(T_{2}T_{1}) = 2R(500  300)= 400R
Two moles of helium gas are taken over the cycle ABCDA, as shown in the PT diagram.
The work done on the gas in taking it from D to A is :
Work done by the system in the isothermal process
Therefore work done on the gas is + 414 R.
Two moles of helium gas are taken over the cycle ABCDA, as shown in the PT diagram.
The net work done on the gas in the cycle ABCDA is :
The net work in the cycle ABCDA is W = W_{AB} + W_{BC}+W_{CD}+W_{DA}
= 693.2 R – 414 R = 279.2 R
One kg of a diatomic gas is at a pressure of 8 × 10^{4}N/m^{2}. The density of the gas is 4kg/m^{3}. What is the energy of the gas due to its thermal motion?
Statement 1 : The temperature dependence of resistance is usually given as R = R_{o} (1 + α Δt). The resistance of a wire changes from 100Ω to 150Ω when its temperature is increased from 27°C to 227°C. This implies that α = 2.5 × 10^{–3}/°C.
Statement 2 : R = R_{o} (1+ α Δt) is valid only when the change in the temperature ΔT is small and ΔR = (R – R_{0}) << R_{o}.
(The relation R = R_{0} (1 +α Δt) is valid for small values of Δt and R_{0} is resistance at 0°C and also (R – R_{0}) should be much smaller than R_{0}. So, statement (1) is wrong but statement (2) is correct.
A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from V to 32 V, the efficiency of the engine is
A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats γ. It is moving with speed v and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by:
Here, work done is zero.
So, loss in kinetic energy = change in internal energy of gas
Three perfect gases at absolute temperatures T_{1}, T_{2} and T_{3} are mixed. The masses of molecules are m_{1}, m_{2} and m_{3} and the number of molecules are n_{1}, n_{2} and n_{3} respectively. Assuming no loss of energy, the final temperature of the mixture is :
Number of moles of first gas = n_{1}/N_{A}
Number of moles of second gas =n_{2}/N_{A}
Number of moles of third gas =n_{3}/N_{A}
If there is no loss of energy then
A Carnot engine operating between temperatures T_{1 }and T_{2} has efficiency 1/6. When T_{2} is lowered by 62 K its efficiency increases to 1/3. Then T_{1} and T_{2 }are, respectively:
Efficiency of engine
100g of water is heated from 30°C to 50°C. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184 J/kg/K):
A wooden wheel of radius R is made of two semicircular part (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area S and length L. L is slightly less than 2πR. To fit the ring on the wheel, it is heated so that its temperature rises by ΔT and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is α, and its Young's modulus is Y, the force that one part of the wheel applies on the other part is :
∴ The ring is pressing the wheel from both sides,
Helium gas goes through a cycle ABCDA (consisting of two isochoric and isobaric lines) as shown in figure Efficiency of this cycle is nearly : (Assume the gas to be close to ideal gas)
Heat given to system =
A liquid in a beaker has temperature θ(t) at time t and θ_{0} is temperature of surroundings, then according to Newton's law of cooling the correct graph between log_{e} (θθ_{0}) and t is :
Newton's law of cooling
Integrating
Which represents an equation of straight line.
Thus the option (a) is correct.
A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be :
on solving we get T_{2} = 750 K
The above pv diagram represents the thermodynamic cycle of an engine, operatingwith an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is
Same as in A 51
If a piece of metal is heated to temperature θ and then allowed to cool in a room which is at temperature θ_{0}, the graph between the temperature T of the metal and time t will be closest to
According to Newton’s law of cooling, the temperature goes on decreasing with time nonlinearly.
The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100ºC is: (For steel Young’s modulus is 2*10^{11}Nm^{2} and coefficient of thermal expansion is 1.1*10^{5 }K^{1 })
Young's modulus Y = stress/strain stress = Y ´ strain
Stress in steel wire = Applied pressure Pressure = stress = Y × strain
= 2.2 × 10^{8} Pa
There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d_{1} and d_{2 }are filled in the tube.Each liquid subtends 90º angle at centre. Radius joining their interface makes an angle a with vertical. Ratio d_{1}/d_{2} is:
Pressure at interface A must be same from both the sides to be in equilibrium.
Three rods of Copper, Brass and Steel are welded together to form a Y shaped structure. Area of cross  section of each rod = 4cm ^{2} . End of copper rod is maintained at 100°C where as ends of brass and steel are kept at 0°C. Lengths of the copper,, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings excepts at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is:
Rate of heat flow is given by,
Where, K = coefficient of thermal conductivity l = length of rod and A = Area of crosssection of rod
If the junction temperature is T, then
One mole of a diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement:
In cyclic process, change in total internal energy is zero.
Where, C_{v} = molar specific heat at constant volume.
A solid body of constant heat capacity 1 J/°C is being heated by keeping it in contact with reservoirs in two ways :
(i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat.
(ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat.
In both the cases body is brought from initial temperature 100°C to final temperature 200°C. Entropy change of the body in the two cases respectively is :
The entropy change of the body in the two cases is same as entropy is a state function.
Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u = U/V∝T^{4}
and pressure p=1/3 (U/V). If the shell now undergoes an adiabatic expansion the relation between T and R is :
Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as Vq, where V is the volume of the gas. The value of q is
'n' moles of an ideal gas undergoes a process A → B as shown in the figure. The maximum temperature of the gas during the process will be :
The equation for the line is
For temperature to be maximum dT/dv= 0
Differentiating e.q. (iii) by 'v' we get
A pendulum clock loses 12 s a day if the temperature is 40°C and gains 4 s a day if the temperature is 20° C. The temperature at which the clock will show correct time, and the coefficient of linear expansion (a) of the metal of the pendulum shaft are respectively :
Time lost/gained per day
An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by PV^{n} = constant, then n is given by (Here C_{P} and C_{V} are molar specific heat at constant pressure and constant volume, respectively) :
For a polytropic process
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