Thermodynamics

In a process, the pressure of a gas is directly proportional to its temperature. Choose the correct options:

A: The process is isochoric.
B: Work done in the process is zero.
C: Internal energy increases with an increase in temperature.

(Shift I - Memory Based)

Assertion: On increasing the pressure, the volume decrease is more in an isothermal process than in an adiabatic process.

Reason: The adiabatic process is governed by the equation:\(P{V}^{\gamma }=\text{constant}\)

(Shift - II Memory Based)

In an adiabatic process, which of the following statements is true ?

[JEE Main 2025, 2 Apr (Shift 1)]

Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4% when heated by 1°C. Its initial temperature must be ;

[JEE Main 2025, 3 Apr (Shift 2)]

Water of mass \(m\) gram is slowly heated to increase the temperature from \({T}_{1}\) to \({T}_{2}\). The change in entropy of the water, given specific heat of water is \(1{\mathrm{Jkg}}^{-1}{\mathrm{K}}^{-1}\), is :

[JEE Main 2025, 23 Jan (Shift 2)]

Initial pressure and volume of a monoatomic ideal gas are P and V. The change in internal energy of this gas in adiabatic expansion to volume \({V}_{\text{final }}=27V\) is _{---------------} J.

[JEE Main 2026, 8 Apr (Shift 2)]

For an ideal monoatomic gas undergoing an isobaric process, what is the ratio \(\frac{\Delta Q}{\Delta U}\)? (Shift I - Memory Based)

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.
Reason (R) : In isothermal process, PV = constant, while in adiabatic process \(P{V}^{\gamma }=\) constant. Here \(\gamma\) is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas.
In the light of the above statements, choose the correct answer from the options given below :

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same P, V, T. Heating is started from left side until pressure changes to \(\frac{27}{8}\mathrm{P}\). If initial volume of each compartment was 9 litres then the final volume in right-hand side compartment is ______ litres. (for this ideal gas \(\frac{{C}_{P}}{{C}_{V}}=1.5\) )

[JEE Main 2026, 6 Apr (Shift 2)]

An ideal gas at 0°C is suddenly compressed to 1/4 times of its initial volume. If the ratio of molar heat capacity at constant pressure to the molar heat capacity at constant volume is 3/2 find the difference between final temperature and initial temperature.

(Shift I Memory Based)

The temperature of a body of mass \(m\) and specific heat capacity \(s\)s is raised slowly from \({T}_{1}\) to \({T}_{2}\)​. The change in entropy of the system is:(Shift - II Memory Based)

An ideal gas at 0°C is suddenly compressed to 1/4 times of its initial volume. If the ratio of molar heat capacity at constant pressure to the molar heat capacity at constant volume is 3/2 find the difference between final temperature and initial temperature.

(Shift I Memory Based)

Given are statements for certain thermodynamic variables,
(A) Internal energy, volume \((\mathrm{V})\) and mass \((\mathrm{M})\) are extensive variables.
(B) Pressure (P), temperature (T) and density ( \(\rho\) ) are intensive variables.
(C) Volume (V), temperature (T) and density ( \(\rho\) ) are intensive variables.
(D) Mass (M), temperature (T) and internal energy are extensive variables.

Choose the correct answer from the options given below :

[JEE Main 2025, 22 Jan (Shift 2)]

Assertion: On increasing the pressure, the volume decrease is more in an isothermal process than in an adiabatic process.

Reason: The adiabatic process is governed by the equation:\(P{V}^{\gamma }=\text{constant}\)

(Shift - II Memory Based)

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of \(\frac{C p}{C v}\) for the gas is:

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases.
Reason (R): Free expansion of an ideal gas is an irreversible and an adiabatic process.
In the light of the above statements, choose the correct answer from the options given below:

For an ideal monoatomic gas undergoing an isobaric process, what is the ratio \(\frac{\Delta Q}{\Delta U}\)? (Shift I - Memory Based)

In a process, the pressure of a gas is directly proportional to its temperature. Choose the correct options:

A: The process is isochoric.
B: Work done in the process is zero.
C: Internal energy increases with an increase in temperature.

(Shift I - Memory Based)

A Carnot engine (E) is working between two temperatures 473 K and 273 K . In a new system two engines - engine \({E}_{1}\) works between 473 K to 373 K and engine \({E}_{2}\) works between 373 K to 273 K . If \({\eta }_{12}\), \({\eta }_{1}\) and \({\eta }_{2}\) are the efficiencies of the engines \(E\), \({E}_{1}\) and \({E}_{2}\), respectively, then

[JEE Main 2025, 28 Jan (Shift 1)]

A total of \(48 \ J\) heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by \(2^{\circ} C\). The work done by the gas is:
Given, \(R =8.3 J K ^{-1} mol ^{-1}\).

An ideal gas expands such that PT³ = constant. The coefficient of volume expansion of the gas is:

[JEE Main 2026, 5 Apr (Shift 2)]

In an adiabatic process, which of the following statements is true ?

[JEE Main 2025, 2 Apr (Shift 1)]

The temperature of a body of mass \(m\) and specific heat capacity \(s\)s is raised slowly from \({T}_{1}\) to \({T}_{2}\)​. The change in entropy of the system is:(Shift - II Memory Based)

An ideal gas exists in a state with pressure \({\mathrm{P}}_{0}\), volume \({\mathrm{V}}_{0}\).It is isothermally expanded to 4 times of its initial volume \(\left({\mathrm{V}}_{0}\right)\), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is :

Consider the following statements:
A. Zeroth law of thermodynamics gives concept of temperature
B. First law of thermodynamics gives concept of internal energy
C. In isothermal expansion of ideal gas, ΔQ ≠ ΔW
D. Product of intensive and extensive variables is extensive
E. The ratio of any extensive variable to mass will be an extensive variable
Choose the correct combination of statements:

[JEE Main 2026, 5 Apr (Shift 1)]

The work done in an adiabatic change in an ideal gas depends upon only :

[JEE Main 2025, 29 Jan (Shift 1)]

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is ____ grams.
(Latent heat of fusion of lead \(=2.5\times {10}^{4}{\mathrm{JKg}}^{-1}\) and specific heat capacity of lead \(=125{\mathrm{JKg}}^{-1}\) \({\mathrm{K}}^{-1}\) )

[JEE Main 2025, 23 Jan (Shift 1)]

In adiabatic process of closed system, work done by the gas depends explicity on

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of \(800{\mathrm{cm}}^{3}\) and temperature \(27^\circ \mathrm{C}\). The change in temperature when the gas is adiabatically compressed to \(200{\mathrm{cm}}^{3}\) is :
(Take \(\gamma =1.5:\gamma\) is the ratio of specific heats at constant pressure and at constant volume)

[JEE Main 2025, 3 Apr (Shift 1)]

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases.
Reason (R): Free expansion of an ideal gas is an irreversible and an adiabatic process.
In the light of the above statements, choose the correct answer from the options given below :

During the melting of a slab of ice at \(273\) K at atmospheric pressure :

Given are statements for certain thermodynamic variables,
(A) Internal energy, volume \((\mathrm{V})\) and mass \((\mathrm{M})\) are extensive variables.
(B) Pressure (P), temperature (T) and density ( \(\rho\) ) are intensive variables.
(C) Volume (V), temperature (T) and density ( \(\rho\) ) are intensive variables.
(D) Mass (M), temperature (T) and internal energy are extensive variables.

Choose the correct answer from the options given below :

[JEE Main 2025, 22 Jan (Shift 2)]

The work done in an adiabatic change in an ideal gas depends upon only :

[JEE Main 2025, 29 Jan (Shift 1)]

A monoatomic gas having \(\gamma =\frac{5}{3}\) is stored in a thermally insulated container and the gas is suddenly compressed to \({\left(\frac{1}{8}\right)}^{\text{th }}\) of its initial volume. The ratio of final pressure and initial pressure is: ( \(\gamma\) is the ratio of specific heats of the gas at constant pressure and at constant volume)

[JEE Main 2025, 8 Apr (Shift 1)]

\(0.08 \ kg\) air is heated at constant volume through \(5^{\circ} C\). The specific heat of air at constant volume is \(0.17 \ kcal / kg ^{\circ} C\) and \(J =4.18\) joule/cal. The change in its internal energy is approximately.

The temperature of 1 mole of an ideal monoatomic gas is increased by \(50^\circ C\) at constant pressure. The total heat added and change in internal energy are \({E}_{1}\) and \({E}_{2}\), respectively. If \(\frac{{E}_{1}}{{E}_{2}}=\frac{x}{9}\) then the value of x is

[

A monoatomic gas having \(\gamma =\frac{5}{3}\) is stored in a thermally insulated container and the gas is suddenly compressed to \({\left(\frac{1}{8}\right)}^{\text{th }}\) of its initial volume. The ratio of final pressure and initial pressure is: ( \(\gamma\) is the ratio of specific heats of the gas at constant pressure and at constant volume)

The pressure and volume of an ideal gas are related as \(PV ^{\frac{3}{2}}= K\) (Constant). The work done when the gas is taken from state \(A \left( P _1, V _1, T _1\right)\) to state \(B \left( P _2, V _2, T _2\right)\) is :

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.
Reason (R) : In isothermal process, PV = constant, while in adiabatic process \(P{V}^{\gamma }=\) constant. Here \(\gamma\) is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas.
In the light of the above statements, choose the correct answer from the options given below :

An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature.
A. The work done by gas during the process is zero.
B. The heat added to gas is different from change in its internal energy
C. The volume of the gas is increased.
D. The internal energy of the gas is increased.
E. The process is isochoric (constant volume process)
Choose the correct answer from the options given below:

[JEE Main 2025, 24 Jan (Shift 1)]

A Carnot engine (E) is working between two temperatures 473 K and 273 K . In a new system two engines - engine \({E}_{1}\) works between 473 K to 373 K and engine \({E}_{2}\) works between 373 K to 273 K . If \({\eta }_{12}\), \({\eta }_{1}\) and \({\eta }_{2}\) are the efficiencies of the engines \(E\), \({E}_{1}\) and \({E}_{2}\), respectively, then

[JEE Main 2025, 28 Jan (Shift 1)]

During the melting of a slab of ice at \(273\) K at atmospheric pressure :

[JEE Main 2025, 3 Apr (Shift 1)]

In adiabatic process of closed system, work done by the gas depends explicity on

Heat is given to an ideal gas in an isothermal process.
A. Internal energy of the gas will decrease.
B. Internal energy of the gas will increase.
C. Internal energy of the gas will not change.
D. The gas will do positive work.
E. The gas will do negative work.

Choose the correct answer from the options given below:

A source supplies heat to a system at the rate of \(1000 W\). If the system performs work at a rate of \(200 W\). The rate at which internal energy of the system increases

A gas is compressed adiabatically, which one of the following statement is NOT true.

[JEE Main 2023, 10 Apr (Shift 2)]

The thermodynamic process, in which internal energy of the system remains constant is

One mole of an ideal gas expands adiabatically from an initial state (T_A, V₀) to final state (T_f, 5V₀). Another mole of the same gas expands isothermally from a different initial state (T_B, V₀) to the same final state (T_f, 5V₀). The ratio of the specific heats at constant pressure and constant volume of this ideal gas is γ. What is the ratio T_A/T_B?

A Carnot engine operating between two reservoirs has efficiency \(\frac{1}{3}\). When the temperature of cold reservoir is raised by \(x\), its efficiency decreases to \(\frac{1}{6}\). The value of \(x\), if the temperature of hot reservoir is \(99^{\circ} C\), will be:

[JEE Main 2023, 1 Feb (Shift 2)]

Heat energy of \(735 J\) is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be:

[JEE Main 2023, 31 Jan (Shift 2)]

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is \(n\). The internal energy of one mole of the gas is \(U_n\) and the speed of sound in the gas is \(\mathrm{v}_n\). At a fixed temperature and pressure, which of the following is the correct option?

[JEE Advanced 2023]

An electric appliance supplies 6000 J/min heat to the system. If the system delivers a power of 90W. How long it would take to increase the internal energy by \(2.5\times {10}^{3}\) J ?

[JEE Main 2021, 26 Aug (Shift 1)]

A diatomic gas (\(\gamma\) = 1.4) does 100 J of work in an isobaric expansion. The heat given to the gas is :

[JEE Main 2024, 08 Apr (Shift 2)]

The efficiency of a carnot engine depends upon

[Re-NEET 2020]

The initial pressure and volume of an ideal gas are \(P_0\) and \(V_0\). The final pressure of the gas when the gas is suddenly compressed to volume \(\frac{V_0}{4}\) will be: (Given \(\gamma=\) ratio of specific heats at constant pressure and at constant volume)

A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is \(\frac{16}{81}\). Then the ratio of \(\frac{C_P}{C_V}\) will be.

[JEE Main 2023, 31 Jan (Shift 2)]

Heat energy of \(735 \ J\) is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be:

[JEE Main 2023, 31 Jan (Shift 2)]

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\).
Assertion A: Efficiency of a reversible heat engine will be highest at \(-273^{\circ} C\) temperature of cold reservoir.
Reason R: The efficiency of a Carnot's engine depends not only on the temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as \(\eta=\left(1-\frac{T_2}{T_1}\right)\).
In the light of the above statements, choose the correct answer from the options given below:

[JEE Main 2023, 30 Jan (Shift 2)]

\(1 g\) of a liquid is converted to vapour at \(3 \times 10^5 Pa\) pressure. If \(10 \%\) of the heat supplied is used for increasing the volume by \(1600 cm ^3\) during this phase change, then the increase in internal energy in the process will be:

One mole of an ideal gas expands adiabatically from an initial state \(\left(T_A, V_0\right)\) to final state \(\left(T_f, 5 V_0\right)\). Another mole of the same gas expands isothermally from a different initial state \(\left(T_B, V_0\right)\) to the same final state \(\left(T_f, 5 V_0\right)\). The ratio of the specific heats at constant pressure and constant volume of this ideal gas is \(\gamma\). What is the ratio \(T_A / T_B\).

[JEE Advanced 2023]

1 kg of water at 100ºC is converted into steam at 100ºC by boiling at atmospheric pressure. The volume of water changes from 1.00 × 10^–3 m³ as a liquid to 1.671 m³ as steam. The change in internal energy of the system during the process will be (Given latent heat of vaporization = 2257 kJ/kg. Atmospheric pressure = 1 × 10⁵ Pa)

[JEE Main 2023, 11 Apr (Shift 1)]

A source supplies heat to a system at the rate of \(1000 W\). If the system performs work at a rate of \(200 W\). The rate at which internal energy of the system increases

[JEE Main 2023, 6 Apr (Shift 1)]

The pressure \((P)\) and temperature \((T)\) relationship of an ideal gas obeys the equation \(P T^2=\) constant. The volume expansion coefficient of the gas will be:

[JEE Main 2023, 30 Jan (Shift 1)]

Given below are two statements:
Statement-I: If heat is added to a system, its temperature must increase.

Statement-II: If positive work is done by a system in a thermodynamic process, its volume must increase.
In the light of the above statements, choose the correct answer from the options given below.

[JEE Main 2023, 8 Apr (Shift 1)]

In thermodynamics , heat and work are :

[JEE Main 2021, 16 Mar (Shift 1)]

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from \(27^{\circ} \mathrm{C}\) to \(37^{\circ} \mathrm{C}\). If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes which of the following is true?

The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from \(0^{\circ} C\) to \(50^{\circ} C\) when no work is done is . ( \(R\) is the universal gas constant)

[JEE Main 2021, 20 Jul (Shift 1)]

\(1 g\) of a liquid is converted to vapour at \(3 \times 10^5 Pa\) pressure. If \(10 \%\) of the heat supplied is used for increasing the volume by \(1600 cm ^3\) during this phase change, then the increase in internal energy in the process will be:

[JEE Main 2023, 24 Jan (Shift 1)]

A gas is compressed adiabatically, which one of the following statement is NOT true.

A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is \(\frac{16}{81}\). Then the ratio of \(\frac{C_P}{C_V}\) will be.

Consider two containers \(A\) and \(B\) containing monoatomic gases at the same Pressure \((P)\), Volume \((V)\) and Temperature ( \(T\) ). The gas in A is compressed isothermally to \(\frac{1}{8}\) of its original volume while the gas \(B\) is compressed adiabatically to \(\frac{1}{8}\) of its original volume. The ratio of final pressure of gas in \(B\) to that of gas in \(A\) is:

[JEE Main 2023, 10 Apr (Shift 1)]

An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is \(S_1\) and that of the other part is \(S_2\). Given that \(S_1>S_2\). If the piston is removed then the total entropy of the system will be:

[JEE Main 2021, 18 Mar (Shift 2)]

The initial pressure and volume of an ideal gas are P₀ and V₀. The final pressure of the gas when the gas is suddenly compressed to volume \(\frac{{V}_{0}}{4}\) will be: (Given γ = ratio of specific heats at constant pressure and at constant volume)

A sample of gas at temperature \(T\) is adiabatically expanded to double its volume. The work done by the gas in the process is \(\left(\right.\) given, \(\left.\gamma=\frac{3}{2}\right)\) :

[JEE Main 2023, 1 Feb (Shift 1)]

A sample of \( 1 \) mole of gas at temperature \( T \) is

adiabatically expanded to double its volume. The

work done by the gas in the process is (given

\( \gamma=\frac{3}{2} \) )

A diatomic gas, having \(\ C_P=\frac{7}{2} R\) and \(\ C_V=\frac{5}{2} R\),is heated at constant pressure. The ratio \(\ d U: d Q: d W\) :

An engine operating between the boiling and freezing points of water will have
1. Efficiency more than \(27 \%\)
2. Efficiency less than the efficiency a Carnot engine operating between the same two temperatures.
3. Efficiency equal to \(27 \%\)
4. Efficiency less than \(27 \%\)

[JEE Main 2023, 12 Apr (Shift 1)]