Heat & Thermodynamics · JEE Main previous year questions

2023 27 questions

1. Q422023 · 13 Apr 2023 · Shift 1

   Under isothermal condition, the pressure of a gas is given by $\mathrm{P}=a{\mathrm{V}}^{-3}$, where $a$ is a constant and $\mathrm{V}$ is the volume of the gas. The bulk modulus at constant temperature is equal to

   1. A.$\frac{\mathrm{P}}{2}$
   2. B.$2\mathrm{P}$
   3. C.$3\mathrm{P}$
   4. D.$\mathrm{P}$
   Show answer

   Answer: C

2. Q342023 · 13 Apr 2023 · Shift 2

   The initial pressure and volume of an ideal gas are ${\mathrm{P}}_0$ and ${\mathrm{V}}_0$. The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_0}{4}$ will be : (Given $\gamma =\text{ratio of specific heats at constant pressure and at constant volume}$)

   1. A.${\mathrm{P}}_0(4{)}^{\frac{1}{\gamma }}$
   2. B.${\mathrm{P}}_0$
   3. C.$4{\mathrm{P}}_0$
   4. D.${\mathrm{P}}_0(4{)}^{\gamma }$
   Show answer

   Answer: D

3. Q482023 · 12 Apr 2023 · Shift 1

   An engine operating between the boiling and freezing points of water will have A. efficiency more than $27\%$. B. efficiency less than the efficiency of a Carnot engine operating between the same two temperatures. C. efficiency equal to $27\%$ D. efficiency less than $27\%$ Choose the correct answer from the options given below:

   1. A.B and C only
   2. B.B and D only
   3. C.B, C and D only
   4. D.A and B only
   Show answer

   Answer: B

4. Q322023 · 11 Apr 2023 · Shift 1

   $1\text{ kg}$ of water at $100^{\circ }\text{C}$ is converted into steam at $100^{\circ }\text{C}$ by boiling at atmospheric pressure. The volume of water changes from $1.00\times 10^{-3}{\text{ m}}^3$ as a liquid to $1.671{\text{ m}}^3$ as steam. The change in internal energy of the system during the process will be (Given latent heat of vaporisation = $2257\text{ kJ/kg}$, Atmospheric pressure = $1\times 10^5\text{ Pa}$)

   1. A.$+2090\text{ kJ}$
   2. B.$-2426\text{ kJ}$
   3. C.$+2476\text{ kJ}$
   4. D.$-2090\text{ kJ}$
   Show answer

   Answer: A

5. Q342023 · 11 Apr 2023 · Shift 2

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

   1. A.Isobaric
   2. B.Isochoric
   3. C.Adiabatic
   4. D.Isothermal
   Show answer

   Answer: D

6. Q362023 · 10 Apr 2023 · Shift 1

   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 in 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

   1. A.$\frac{1}{8}$
   2. B.$8^{\frac{3}{2}}$
   3. C.4
   4. D.8
   Show answer

   Answer: C

7. Q352023 · 10 Apr 2023 · Shift 2

   A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,

   1. A.4RT
   2. B.16RT
   3. C.8RT
   4. D.11RT
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   Answer: D

8. Q382023 · 10 Apr 2023 · Shift 2

   A gas is compressed adiabatically, which one of the following statements is NOT true?

   1. A.There is no heat supplied to the system
   2. B.The temperature of the gas increases.
   3. C.There is no change in the internal energy
   4. D.The change in the internal energy is equal to the work done on the gas.
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   Answer: C

9. Q372023 · 8 Apr 2023 · 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

   1. A.Both Statement I and Statement II are true
   2. B.Statement I is false but Statement II is true
   3. C.Statement I is true but Statement II is false
   4. D.Both Statement I and Statement II are false
   Show answer

   Answer: B

10. Q502023 · 8 Apr 2023 · Shift 2

    Work done by a Carnot engine operating between temperatures $127^{\circ }\mathrm{C}$ and $27^{\circ }\mathrm{C}$ is $2\mathrm{kJ}$. The amount of heat transferred to the engine by the reservoir is :

    1. A.$8\mathrm{kJ}$
    2. B.$2\mathrm{kJ}$
    3. C.$4\mathrm{kJ}$
    4. D.$2.67\mathrm{kJ}$
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    Answer: A

11. Q352023 · 6 Apr 2023 · Shift 1

    A source supplies heat to a system at the rate of $1000\text{ W}$. If the system performs work at a rate of $200\text{ W}$. The rate at which internal energy of the system increases is

    1. A.$600\text{ W}$
    2. B.$1200\text{ W}$
    3. C.$500\text{ W}$
    4. D.$800\text{ W}$
    Show answer

    Answer: D

12. Q432023 · 1 Feb 2023 · Shift 1

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

    1. A.$W=TR[\sqrt{2}-2]$
    2. B.$W=\frac{T}{R}[\sqrt{2}-2]$
    3. C.$W=\frac{R}{T}[2-\sqrt{2}]$
    4. D.$W=RT[2-\sqrt{2}]$
    Show answer

    Answer: D

13. Q452023 · 31 Jan 2023 · Shift 1
    
    1. A.$6\text{ J}$
    2. B.$4.5\text{ J}$
    3. C.zero
    4. D.$-4.5\text{ J}$
    Show answer

    Answer: B

14. Q472023 · 31 Jan 2023 · Shift 1

    If a source of electromagnetic radiation having power $15\text{ kW}$ produces $10^{16}$ photons per second, the radiation belongs to a part of spectrum is. (Take Planck constant $h=6\times 10^{-34}\text{ Js}$ )

    1. A.Gamma rays
    2. B.Radio waves
    3. C.Micro waves
    4. D.Ultraviolet rays
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    Answer: A

15. Q342023 · 31 Jan 2023 · Shift 2

    If the two metals A and B are exposed to radiation of wavelength $350\text{ nm}$. The work functions of metals A and B are $4.8\text{ eV}$ and $2.2\text{ eV}$. Then choose the correct option.

    1. A.Metal B will not emit photo-electrons
    2. B.Both metals A and B will not emit photo-electrons
    3. C.Metal A will not emit photo-electrons
    4. D.Both metals A and B will emit photo-electrons
    Show answer

    Answer: C

16. Q412023 · 31 Jan 2023 · Shift 2

    A hypothetical gas expands adiabatically such that its volume changes from 8 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 $\frac{\mathrm{Cp}}{\mathrm{Cv}}$ will be.

    1. A.$\frac{3}{1}$
    2. B.$\frac{4}{3}$
    3. C.$\frac{1}{2}$
    4. D.$\frac{3}{2}$
    Show answer

    Answer: B

17. Q512023 · 31 Jan 2023 · Shift 2· Numerical answer

    A water heater of power $2000\text{ W}$ is used to heat water. The specific heat capacity of water is $4200{\text{ J kg}}^{-1}{\text{ K}}^{-1}$. The efficiency of heater is $70\%$. Time required to heat $2\text{ kg}$ of water from $10^{\circ }\text{C}$ to $60^{\circ }\text{C}$ is ___________ s. (Assume that the specific heat capacity of water remains constant over the temperature range of the water).

    Show answer

    Answer: 300

18. Q392023 · 30 Jan 2023 · Shift 1

    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 :

    1. A.B and D only
    2. B.C and E only
    3. C.A and E only
    4. D.C and D only
    Show answer

    Answer: D

19. Q352023 · 29 Jan 2023 · Shift 1

    Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If $dQ$ and $dW$ represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics $dQ=dU-dW$. Reason R: First law of thermodynamics is based on law of conservation of energy. In the light of the above statements, choose the correct answer from the options given below:

    1. A.Both A and R are correct but R is not the correct explanation of A
    2. B.Both A and R are correct and R is the correct explanation of A
    3. C.A is correct but R is not correct
    4. D.A is not correct but R is correct
    Show answer

    Answer: B

20. Q352023 · 29 Jan 2023 · Shift 2

    Heat energy of 184 kJ is given to ice of mass 600 g at $-12^{\circ }\mathrm{C}$. Specific heat of ice is $2222.3\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}{}^{\circ }{\mathrm{C}}^{-1}$ and latent heat of ice is $336\mathrm{kJ}\mathrm{k}{\mathrm{g}}^{-1}$ A. Final temperature of system will be $0^{\circ }\mathrm{C}$. B. Final temperature of the system will be greater than $0^{\circ }\mathrm{C}$. C. The final system will have a mixture of ice and water in the ratio of 5 : 1. D. The final system will have a mixture of ice and water in the ratio of 1 : 5. E. The final system will have water only. Choose the correct answer from the options given below :

    1. A.A and E only
    2. B.B and D only
    3. C.A and C only
    4. D.A and D only
    Show answer

    Answer: D

21. Q472023 · 25 Jan 2023 · Shift 1

    A Carnot engine with efficiency 50% takes heat from a source at 600 K. In order to increase the efficiency to 70%, keeping the temperature of sink same, the new temperature of the source will be :

    1. A.300 K
    2. B.1000 K
    3. C.900 K
    4. D.360 K
    Show answer

    Answer: B

22. Q342023 · 25 Jan 2023 · Shift 2

    Match List I with List II $$\begin{array}{llll}& \text{List I}& & \text{List II}\\ \text{A.}& \text{Isothermal Process}& \text{I.}& \text{Work done by the gas decreases internal energy}\\ \text{B.}& \text{Adiabatic Process}& \text{II.}& \text{No change in internal energy}\\ \text{C.}& \text{Isochoric Process}& \text{III.}& \text{The heat absorbed goes partly to increase internal energy and partly to do work}\\ \text{D.}& \text{Isobaric Process}& \text{IV.}& \text{No work is done on or by the gas}\end{array}$$ Choose the correct answer from the options given below :

    1. A.A-I, B-II, C-IV, D-III
    2. B.A-II, B-I, C-III, D-IV
    3. C.A-II, B-I, C-IV, D-III
    4. D.A-I, B-II, C-III, D-IV
    Show answer

    Answer: C

23. Q452023 · 25 Jan 2023 · Shift 2

    According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-

    1. A.$\frac{9}{2}R$
    2. B.$\frac{5}{2}R$
    3. C.$\frac{3}{2}R$
    4. D.$\frac{7}{2}R$
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    Answer: D

24. Q412023 · 24 Jan 2023 · Shift 1

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

    1. A.$4800\mathrm{J}$
    2. B.$4320\mathrm{J}$
    3. C.$432000\mathrm{J}$
    4. D.$4.32\times 10^8\mathrm{J}$
    Show answer

    Answer: B

25. Q542023 · 24 Jan 2023 · Shift 1· Numerical answer

    A hole is drilled in a metal sheet. At $27^{\circ }\mathrm{C}$, the diameter of hole is $5\mathrm{cm}$. When the sheet is heated to $177^{\circ }\mathrm{C}$, the change in the diameter of hole is $d\times 10^{-3}\mathrm{cm}$. The value of d will be ____ if coefficient of linear expansion of the metal is $1.6\times 10^{-5}{/}^{\circ }\mathrm{C}$.

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    Answer: 12