Heat & Thermodynamics · JEE Main previous year questions

In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation will be:

1. A.$\frac{25}{16}\lambda$
2. B.$\frac{27}{20}\lambda$
3. C.$\frac{16}{25}\lambda$
4. D.$\frac{20}{27}\lambda$

One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, $27^{\circ }C$. The work done on the gas will be :

1. A.$300R$
2. B.$300R\ln 6$
3. C.$300R\ln 2$
4. D.$300R\ln 7$

A Carnot's engine works as a refrigerator between 250 K and 300 K. It receives 500 cal heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is :

1. A.$420J$
2. B.$772J$
3. C.$2100J$
4. D.$2520J$

Two moles of an ideal monatomic gas occupies a volume V at $27^{\circ }\mathrm{C}$. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

1. A.(a) 195 K (b) 2.7 kJ
2. B.(a) 189 K (b) 2.7 kJ
3. C.(a) 195 K (b) $-2.7\mathrm{kJ}$
4. D.(a) 189 K (b) $-2.7\mathrm{kJ}$

In an experiment, a sphere of aluminium of mass 0.20 kg is heated upto $150^{\circ }\mathrm{C}$. Immediately, it is put into water of volume 150 cc at $27^{\circ }\mathrm{C}$ kept in a calorimeter of water equivalent to 0.025 kg. Final temperature of the system is $40^{\circ }\mathrm{C}$. The specific heat of aluminium is : (take 4.2 Joule = 1 calorie)

1. A.$378J/kg-{}^{\circ }\mathrm{C}$
2. B.$315J/kg-{}^{\circ }\mathrm{C}$
3. C.$476J/kg-{}^{\circ }\mathrm{C}$
4. D.$434J/kg-{}^{\circ }\mathrm{C}$

An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (${\mathrm{C}}_{\mathrm{p}}$ ) and at constant volume (${\mathrm{C}}_{\mathrm{v}}$) is :

1. A.$6$
2. B.$\frac{7}{2}$
3. C.$\frac{5}{2}$
4. D.$\frac{7}{5}$

1. A.$0.24$
2. B.$0.15$
3. C.$0.32$
4. D.$0.08$

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 $P{V}^n=\text{constant}$, then $n$ is given by (Here $C_p$ and $C_v$ are molar specific heat at constant pressure and constant volume, respectively:

1. A.$n=\frac{C_p-C}{C-C_v}$
2. B.$n=\frac{C-C_v}{C-C_p}$
3. C.$n=\frac{C_p}{C_v}$
4. D.$n=\frac{C-C_p}{C-C_v}$

Radiation of wavelength $\lambda$, is incident on a photocell. The fastest emitted electron has speed $v$. If the wavelength is changed to $\frac{3\lambda }{4}$, the speed of the fastest emitted electron will be:

1. A.$=v{\left(\frac{4}{3}\right)}^{\frac{1}{2}}$
2. B.$=v{\left(\frac{3}{4}\right)}^{\frac{1}{2}}$
3. C.$>v{\left(\frac{4}{3}\right)}^{\frac{1}{2}}$
4. D.$<v{\left(\frac{4}{3}\right)}^{\frac{1}{2}}$

Arrange the following electromagnetic radiations per quantum in the order of increasing energy : A : Blue light           B : Yellow light C : X-ray                 D : Radiowave.

1. A.C, A, B, D
2. B.B, A, D, C
3. C.D, B, A, C
4. D.A, B, D, C

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 $u=\frac{U}{V}\propto T^4$ and pressure $p=\frac{1}{3}\left(\frac{U}{V}\right)$. If the shell now undergoes an adiabatic expansion the relation between $T$ and $R$ is:

1. A.$T\propto \frac{1}{R}$
2. B.$T\propto \frac{1}{R^3}$
3. C.$T\propto e^{-R}$
4. D.$T\propto e^{-3R}$

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 $V^q$, where $V$ is the volume of the gas. The value of $q$ is: $\left(\gamma =\frac{C_p}{C_v}\right)$

1. A.$\frac{\gamma +1}{2}$
2. B.$\frac{\gamma -1}{2}$
3. C.$\frac{3\gamma +5}{6}$
4. D.$\frac{3\gamma -5}{6}$

1. A.The change in internal energy in whole cyclic process is $250R$.
2. B.The change in internal energy in the process $CA$ is $700R$.
3. C.The change in internal energy in the process $AB$ is $-350R$.
4. D.The change in internal energy in the process $BC$ is $-500R$.

An ideal monatomic gas with pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $2V$ and a final pressure $P_i$. If the same gas is expanded adiabatically to a volume $2V$, the final pressure is $P_a$. The ratio $\frac{P_a}{P_i}$ is

1. A.$2^{-1/3}$
2. B.$2^{1/3}$
3. C.$2^{2/3}$
4. D.$2^{-2/3}$

The door of a working refrigerator is left open in a well insulated room. The temperature of air in the room will

1. A.decrease
2. B.increase in winters and decrease in summers
3. C.remain the same
4. D.increase

A given ideal gas with $\gamma =\frac{C_p}{C_v}=1.5$ at a temperature $T$. If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be

1. A.$2\sqrt{2}T$
2. B.$4T$
3. C.$2T$
4. D.$8T$

This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: In an adiabatic process, change in internal energy of a gas is equal to work done on/by the gas in the process. Statement 2: The temperature of a gas remains constant in an adiabatic process.

1. A.Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
2. B.Statement 1 is true, Statement 2 is false.
3. C.Statement 1 is false, Statement 2 is true.
4. D.Statement 1 is false, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

If a source of power $4\mathrm{kW}$ produces $10^{20}$ photons/second, the radiation belongs to a part of the spectrum called

1. A.$X$-rays
2. B.ultraviolet rays
3. C.microwaves
4. D.$\gamma$ - rays

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 $32V$, the efficiency of the engine is

1. A.0.5
2. B.0.75
3. C.0.99
4. D.0.25

Assuming the Sun to be a spherical body of radius $R$ at a temperature of $TK$, evaluate the total radiant power incident on Earth at a distance $r$ from the Sun Where $r_0$ is the radius of the Earth and $\sigma$ is Stefan's constant.

1. A.$4\pi r_0^2{R}^2\sigma \frac{T^4}{r^2}$
2. B.$\pi r_0^2{R}^2\sigma \frac{T^4}{r^2}$
3. C.$r_0^2{R}^2\sigma \frac{T^4}{4\pi r^2}$
4. D.$R^2\sigma \frac{T^4}{r^2}$

The work of $146kJ$ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by $7^{\circ }C$. The gas is $(R=8.3Jmo{l}^{-1}{K}^{-1})$

1. A.diatomic
2. B.triatomic
3. C.a mixture of monoatomic and diatomic
4. D.monoatomic

Which of the following is incorrect regarding the first law of thermodynamics?

1. A.It is a restatement of the principle of conservation of energy
2. B.It is not applicable to any cyclic process
3. C.It introduces the concept of the entropy
4. D.It introduces the concept of the internal energy

The intensity of gamma radiation from a given source is I. On passing through $36\mathrm{mm}$ of lead, it is reduced to $\frac{1}{8}$. The thickness of lead which will reduce the intensity to $\frac{1}{2}$ will be

1. A.$9\mathrm{mm}$
2. B.$6\mathrm{mm}$
3. C.$12\mathrm{mm}$
4. D.$18\mathrm{mm}$

One mole of ideal monatomic gas $(\gamma =5/3)$ is mixed with one mole of diatomic gas $(\gamma =7/5)$. What is $\gamma$ for the mixture? $\gamma$ Denotes the ratio of specific heat at constant pressure, to that at constant volume

1. A.$35/23$
2. B.$23/15$
3. C.$3/2$
4. D.$4/3$

Which of the following statements is correct for any thermodynamic system ?

1. A.The change in entropy can never be zero
2. B.Internal energy and entropy are state functions
3. C.The internal energy changes in all processes
4. D.The work done in an adiabatic process is always zero