Heat & Thermodynamics · JEE Main previous year questions

2024 17 questions

1. Q352024 · 9 Apr 2024 · Shift 1

   The volume of an ideal gas ($\gamma =1.5$) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is :

   1. A.$\frac{4}{5}$
   2. B.$\frac{8}{5\sqrt{5}}$
   3. C.$\frac{2}{\sqrt{5}}$
   4. D.$\frac{16}{25}$
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   Answer: B

2. Q412024 · 9 Apr 2024 · Shift 1

   A sample of $1\text{ mole}$ gas at temperature $T$ is adiabatically expanded to double its volume. If adiabatic constant for the gas is $\gamma =\frac{3}{2}$, then the work done by the gas in the process is :

   1. A.$\mathrm{R}T[2+\sqrt{2}]$
   2. B.$\mathrm{R}T[2-\sqrt{2}]$
   3. C.$\frac{\mathrm{R}}{T}[2-\sqrt{2}]$
   4. D.$\frac{T}{\mathrm{R}}[2+\sqrt{2}]$
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   Answer: B

3. Q422024 · 8 Apr 2024 · Shift 1

   A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature ($27^{\circ }\text{C}$). The ratio of specific heat of gases at constant volume respectively is:

   1. A.$\frac{3}{2}$
   2. B.$\frac{3}{5}$
   3. C.$\frac{7}{5}$
   4. D.$\frac{5}{3}$
   Show answer

   Answer: B

4. Q502024 · 8 Apr 2024 · Shift 1
   
   1. A.$\frac{V_a}{V_d}\ne \frac{V_b}{V_c}$
   2. B.$\frac{V_a}{V_d}={\left(\frac{V_b}{V_c}\right)}^{-1}$
   3. C.$\frac{V_a}{V_d}=\frac{V_b}{V_c}$
   4. D.$\frac{V_a}{V_d}={\left(\frac{V_b}{V_c}\right)}^2$
   Show answer

   Answer: C

5. Q372024 · 8 Apr 2024 · Shift 2

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

   1. A.$150\mathrm{J}$
   2. B.$490\mathrm{J}$
   3. C.$350\mathrm{J}$
   4. D.$250\mathrm{J}$
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   Answer: C

6. Q352024 · 5 Apr 2024 · Shift 2

   During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $\frac{{\mathrm{C}}_{\mathrm{p}}}{{\mathrm{C}}_{\mathrm{v}}}$ for the gas is :

   1. A.$\frac{5}{3}$
   2. B.$\frac{3}{2}$
   3. C.$\frac{7}{5}$
   4. D.$\frac{9}{7}$
   Show answer

   Answer: B

7. Q352024 · 4 Apr 2024 · Shift 2

   A sample of gas at temperature $T$ is adiabatically expanded to double its volume. Adiabatic constant for the gas is $\gamma =3/2$. The work done by the gas in the process is: $(\mu =1\text{ mole})$

   1. A.$RT[2\sqrt{2}-1]$
   2. B.$RT[2-\sqrt{2}]$
   3. C.$RT[1-2\sqrt{2}]$
   4. D.$RT[\sqrt{2}-2]$
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   Answer: B

8. Q342024 · 1 Feb 2024 · Shift 1

   Two moles of a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is :

   1. A.$\frac{3}{2}\mathrm{R}$
   2. B.$\frac{7}{4}\mathrm{R}$
   3. C.$\frac{5}{2}\mathrm{R}$
   4. D.$\frac{9}{4}\mathrm{R}$
   Show answer

   Answer: D

9. Q402024 · 1 Feb 2024 · Shift 2

   A diatomic gas $(\gamma =1.4)$ does $200\text{ J}$ of work when it is expanded isobarically. The heat given to the gas in the process is :

   1. A.$800\text{ J}$
   2. B.$600\text{ J}$
   3. C.$700\text{ J}$
   4. D.$850\text{ J}$
   Show answer

   Answer: C

10. Q602024 · 1 Feb 2024 · Shift 2· Numerical answer

    A particular hydrogen-like ion emits the radiation of frequency $3\times 10^{15}\text{ Hz}$ when it makes transition from $n=2$ to $n=1$. The frequency of radiation emitted in transition from $n=3$ to $n=1$ is $\frac{x}{9}\times 10^{15}\text{ Hz}$, when $x=$ ________ .

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    Answer: 32

11. Q332024 · 31 Jan 2024 · Shift 1
    
    1. A.$P_2>P_1$
    2. B.$P_1>P_2$
    3. C.$P_1=P_2$
    4. D.$P_2\ge P_1$
    Show answer

    Answer: B

12. Q412024 · 31 Jan 2024 · Shift 2

    A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

    1. A.29 RT
    2. B.27 RT
    3. C.20 RT
    4. D.21 RT
    Show answer

    Answer: B

13. Q392024 · 30 Jan 2024 · Shift 1
    
    1. A.$C_P>C_B>C_A>C_V$
    2. B.$C_P>C_V>C_A=C_B$
    3. C.$C_A=0\text{ and }{C}_B=\infty$
    4. D.$C_A=\infty ,C_B=0$
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    Answer: A

14. Q382024 · 29 Jan 2024 · Shift 1
    
    1. A.$800\text{ J}$
    2. B.$2200\text{ J}$
    3. C.$33800\text{ J}$
    4. D.$1200\text{ J}$
    Show answer

    Answer: A

15. Q402024 · 27 Jan 2024 · Shift 1

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

    1. A.$318\text{ J}$
    2. B.$298\text{ J}$
    3. C.$284\text{ J}$
    4. D.$142\text{ J}$
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    Answer: C

16. Q402024 · 27 Jan 2024 · Shift 2

    During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of $\frac{\text{Cp}}{\text{Cv}}$ for the gas is :

    1. A.$\frac{7}{5}$
    2. B.$\frac{3}{2}$
    3. C.$\frac{9}{7}$
    4. D.$\frac{5}{3}$
    Show answer

    Answer: B

17. Q602024 · 27 Jan 2024 · Shift 2· Numerical answer

    If Rydberg's constant is $R$, the longest wavelength of radiation in Paschen series will be $\frac{\alpha }{7R}$, where $\alpha =$ _______.

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    Answer: 144