Heat & Thermodynamics · JEE Main previous year questions

2022 24 questions

1. Q532022 · 29 Jul 2022 · Shift 1· Numerical answer

   The pressure ${\mathrm{P}}_1$ and density ${\mathrm{d}}_1$ of diatomic gas $\left(\gamma =\frac{7}{5}\right)$ changes suddenly to ${\mathrm{P}}_2\left(>{\mathrm{P}}_1\right)$ and ${\mathrm{d}}_2$ respectively during an adiabatic process. The temperature of the gas increases and becomes ____ times of its initial temperature. (given $\frac{{\mathrm{d}}_2}{{\mathrm{d}}_1}=32$)

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   Answer: 4

2. Q542022 · 29 Jul 2022 · Shift 1· Numerical answer

   One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $\frac{{\alpha }^2}{4}\mathrm{R}J/mol\mathrm{K}$; then the value of $\alpha$ will be ____. (Assume that the given diatomic gas has no vibrational mode).

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   Answer: 3

3. Q462022 · 29 Jul 2022 · Shift 2
   
   1. A.$-450\mathrm{J}$
   2. B.$450\mathrm{J}$
   3. C.$900\mathrm{J}$
   4. D.$1350\mathrm{J}$
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   Answer: B

4. Q522022 · 29 Jul 2022 · Shift 2· Numerical answer

   Nearly $10\%$ of the power of a $110\mathrm{W}$ light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of $1\mathrm{m}$ from the bulb to a distance of $5\mathrm{m}$ is $a\times 10^{-2}W/{\mathrm{m}}^2$. The value of 'a' will be ____.

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   Answer: 84

5. Q482022 · 28 Jul 2022 · Shift 1

   A Carnot engine has efficiency of $50\%$. If the temperature of sink is reduced by $40^{\circ }\text{C}$, its efficiency increases by $30\%$. The temperature of the source will be:

   1. A.$166.7\text{ K}$
   2. B.$255.1\text{ K}$
   3. C.$266.7\text{ K}$
   4. D.$367.7\text{ K}$
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   Answer: C

6. Q312022 · 28 Jul 2022 · Shift 2

   Consider the efficiency of Carnot's engine is given by $\eta =\frac{\alpha \beta }{\sin \theta }{\log }_e\frac{\beta x}{kT}$, where $\alpha$ and $\beta$ are constants. If T is temperature, k is Boltzmann constant, $\theta$ is angular displacement and x has the dimensions of length. Then, choose the incorrect option :

   1. A.Dimensions of $\beta$ is same as that of force.
   2. B.Dimensions of ${\alpha }^{-1}x$ is same as that of energy.
   3. C.Dimensions of ${\eta }^{-1}\sin \theta$ is same as that of $\alpha \beta$.
   4. D.Dimensions of $\alpha$ is same as that of $\beta$.
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   Answer: D

7. Q382022 · 27 Jul 2022 · Shift 1

   Read the following statements : A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice. B. Two bodies $P$ and $Q$ having equal surface areas are maintained at temperature $10^{\circ }\text{C}$ and $20^{\circ }\text{C}$. The thermal radiation emitted in a given time by P and Q are in the ratio $1:1.15$. C. A Carnot Engine working between $100\text{ K}$ and $400\text{ K}$ has an efficiency of $75\%$. D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice. Choose the correct answer from the options given below :

   1. A.A, B, C only
   2. B.A, B only
   3. C.A, C only
   4. D.B, C, D only
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   Answer: A

8. Q462022 · 27 Jul 2022 · Shift 2
   
   1. A.same as the $1^{\mathrm{st}}$ case.
   2. B.always greater than the $1^{\mathrm{st}}$ case.
   3. C.always less than the $1^{\mathrm{st}}$ case.
   4. D.may increase or decrease with respect to the $1^{\mathrm{st}}$ case.
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   Answer: A

9. Q502022 · 25 Jul 2022 · Shift 2

   Let ${\eta }_1$ is the efficiency of an engine at $T_1=447^{\circ }\text{C}$ and $T_2=147^{\circ }\text{C}$ while ${\eta }_2$ is the efficiency at $T_1=947^{\circ }\text{C}$ and $T_2=47^{\circ }\text{C}$. The ratio $\frac{{\eta }_1}{{\eta }_2}$ will be :

   1. A.0.41
   2. B.0.56
   3. C.0.73
   4. D.0.70
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   Answer: B

10. Q532022 · 25 Jul 2022 · Shift 2· Numerical answer

    A block of ice of mass $120\text{ g}$ at temperature $0^{\circ }\text{C}$ is put in $300\text{ g}$ of water at $25^{\circ }\text{C}$. The x g of ice melts as the temperature of the water reaches $0^{\circ }\text{C}$. The value of x is ___________. [Use specific heat capacity of water $=4200{\text{ Jkg}}^{-1}{\text{K}}^{-1}$, Latent heat of ice $=3.5\times 10^5{\text{ Jkg}}^{-1}$]

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    Answer: 90

11. Q412022 · 30 Jun 2022 · Shift 1

    A sample of monoatomic gas is taken at initial pressure of $75\text{ kPa}$. The volume of the gas is then compressed from $1200{\text{ cm}}^3$ to $150{\text{ cm}}^3$ adiabatically. In this process, the value of workdone on the gas will be :

    1. A.$79\text{ J}$
    2. B.$405\text{ J}$
    3. C.$4050\text{ J}$
    4. D.$9590\text{ J}$
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    Answer: B

12. Q382022 · 28 Jun 2022 · Shift 2
    
    1. A.$20\mathrm{J}$
    2. B.$30\mathrm{J}$
    3. C.$-30\mathrm{J}$
    4. D.$-60\mathrm{J}$
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    Answer: B

13. Q582022 · 27 Jun 2022 · Shift 1· Numerical answer

    In a carnot engine, the temperature of reservoir is $527^{\circ }\mathrm{C}$ and that of sink is $200\mathrm{K}$. If the work done by the engine when it transfers heat from reservoir to sink is $12000\mathrm{kJ}$, the quantity of heat absorbed by the engine from reservoir is ____ $\times 10^6\mathrm{J}$.

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    Answer: 16

14. Q392022 · 27 Jun 2022 · Shift 2

    A lead bullet penetrates into a solid object and melts. Assuming that $40\%$ of its kinetic energy is used to heat it, the initial speed of bullet is : (Given : initial temperature of the bullet $=127^{\circ }\text{C}$, Melting point of the bullet $=327^{\circ }\text{C}$, Latent heat of fusion of lead $=2.5\times 10^4{\text{ J kg}}^{-1}$, Specific heat capacity of lead $=125\text{ J/kg K}$)

    1. A.$125{\text{ ms}}^{-1}$
    2. B.$500{\text{ ms}}^{-1}$
    3. C.$250{\text{ ms}}^{-1}$
    4. D.$600{\text{ ms}}^{-1}$
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    Answer: B

15. Q532022 · 27 Jun 2022 · Shift 2· Numerical answer

    A diatomic gas ($\gamma =1.4$) does $400\text{J}$ of work when it is expanded isobarically. The heat given to the gas in the process is ________ J.

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    Answer: 1400

16. Q382022 · 26 Jun 2022 · Shift 1

    A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel, temperature of the gas increases by : (R = universal gas constant)

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

17. Q482022 · 26 Jun 2022 · Shift 1

    The efficiency of a Carnot's engine, working between steam point and ice point, will be :

    1. A.26.81%
    2. B.37.81%
    3. C.47.81%
    4. D.57.81%
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    Answer: A

18. Q542022 · 26 Jun 2022 · Shift 2· Numerical answer

    A geyser heats water flowing at a rate of 2.0 kg per minute from $30^{\circ }\text{C}$ to $70^{\circ }\text{C}$. If geyser operates on a gas burner, the rate of combustion of fuel will be ________ ${\text{g min}}^{-1}$. [Heat of combustion $=8\times 10^3{\text{ Jg}}^{-1}$, Specific heat of water $=4.2{\text{ Jg}}^{-1}{}^{\circ }{\text{C}}^{-1}$]

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    Answer: 42

19. Q602022 · 25 Jun 2022 · Shift 1· Numerical answer

    A steam engine intakes $50\text{ g}$ of steam at $100^{\circ }\text{C}$ per minute and cools it down to $20^{\circ }\text{C}$. If latent heat of vaporization of steam is $540{\text{ cal g}}^{-1}$, then the heat rejected by the steam engine per minute is $\underline{}\times 10^3\text{ cal}$. (Given : specific heat capacity of water : $1{\text{ cal g}}^{-1}{}^{\circ }{\mathrm{C}}^{-1}$)

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    Answer: 31

20. Q352022 · 25 Jun 2022 · Shift 2

    A copper block of mass $5.0\mathrm{kg}$ is heated to a temperature of $500^{\circ }\mathrm{C}$ and is placed on a large ice block. What is the maximum amount of ice that can melt? [Specific heat of copper : $0.39\mathrm{J}{\mathrm{g}}^{-1}{}^{\circ }{\mathrm{C}}^{-1}$ and latent heat of fusion of water : $335\mathrm{J}{\mathrm{g}}^{-1}$]

    1. A.$1.5\mathrm{kg}$
    2. B.$5.8\mathrm{kg}$
    3. C.$2.9\mathrm{kg}$
    4. D.$3.8\mathrm{kg}$
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    Answer: C

21. Q362022 · 25 Jun 2022 · Shift 2

    The ratio of specific heats $\left(\frac{C_P}{C_V}\right)$ in terms of degree of freedom (f) is given by :

    1. A.$\left(1+\frac{f}{3}\right)$
    2. B.$\left(1+\frac{2}{f}\right)$
    3. C.$\left(1+\frac{f}{2}\right)$
    4. D.$\left(1+\frac{1}{f}\right)$
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    Answer: B

22. Q432022 · 24 Jun 2022 · Shift 2

    A $100\mathrm{g}$ of iron nail is hit by a $1.5\mathrm{kg}$ hammer striking at a velocity of $60\mathrm{m}{\mathrm{s}}^{-1}$. What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail? [Specific heat capacity of iron = $0.42\mathrm{J}{\mathrm{g}}^{-1}{}^{\circ }{\mathrm{C}}^{-1}$]

    1. A.$675^{\circ }\mathrm{C}$
    2. B.$1600^{\circ }\mathrm{C}$
    3. C.$16.07^{\circ }\mathrm{C}$
    4. D.$6.75^{\circ }\mathrm{C}$
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    Answer: C

23. Q502022 · 24 Jun 2022 · Shift 2

    A Carnot engine takes $5000\mathrm{kcal}$ of heat from a reservoir at $727^{\circ }\mathrm{C}$ and gives heat to a sink at $127^{\circ }\mathrm{C}$. The work done by the engine is

    1. A.$3\times 10^6\mathrm{J}$
    2. B.Zero
    3. C.$12.6\times 10^6\mathrm{J}$
    4. D.$8.4\times 10^6\mathrm{J}$
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    Answer: C

24. Q602022 · 24 Jun 2022 · Shift 2· Numerical answer
    
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    Answer: 16