Heat & Thermodynamics · JEE Main previous year questions

Match the LIST-I with LIST-II \begin{tabular}{|l|l|l|l|} \hline \textbf{LIST-I} & & \textbf{LIST-II} & \\ \hline A. & Boltzmann constant & I & ${\mathrm{ML}}^2{\mathrm{T}}^{-1}$ \\ B & Coefficient of viscosity & II & ${\mathrm{MLT}}^{-3}{\mathrm{K}}^{-1}$ \\ C & Planck's constant & III & ${\mathrm{ML}}^2{\mathrm{T}}^{-2}{\mathrm{K}}^{-1}$ \\ D & Thermal conductivity & IV & ${\mathrm{ML}}^{-1}{\mathrm{T}}^{-1}$ \\ \hline \end{tabular} Choose the correct answer from the options given below:

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

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

1. A.The internal energy of the gas decreases as the temperature increases
2. B.The molar heat capacity is zero
3. C.Work done by the gas equals the increase in internal energy
4. D.The molar heat capacity is infinite

${\gamma }_{\mathrm{A}}$ is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. ${\gamma }_B$ is the specific heat ratio of polyatomic gas $B$ having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If $\frac{{\gamma }_{\mathrm{A}}}{{\gamma }_B}=\left(1+\frac{1}{n}\right)$, then the value of $n$ is _________ .

Match List - I with List - II. $$\begin{array}{llll}& \text{List - I}& & List-II\\ \text{(A)}& \text{Heat capacity of body}& \text{(I)}& \mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}\\ \text{(B)}& \text{Specific heat capacity of body}& \text{(II)}& \mathrm{J}{\mathrm{K}}^{-1}\\ \text{(C)}& \text{Latent heat}& \text{(III)}& \mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}{\mathrm{K}}^{-1}\\ \text{(D)}& \text{Thermal conductivity}& \text{(IV)}& \mathrm{J}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}{\mathrm{s}}^{-1}\end{array}$$ Choose the correct answer from the options given below :

1. A.(A)-(IV), (B)-(III), (C)-(II), (D)-(I)
2. B.(A)-(III), (B)-(I), (C)-(II), (D)-(IV)
3. C.(A)-(III), (B)-(IV), (C)-(I), (D)-(II)
4. D.(A)-(II), (B)-(III), (C)-(I), (D)-(IV)

Identify the characteristics of an adiabatic process in a monoatomic gas. (A) Internal energy is constant. (B) Work done in the process is equal to the change in internal energy. (C) The product of temperature and volume is a constant. (D) The product of pressure and volume is a constant. (E) The work done to change the temperature from ${\mathrm{T}}_1$ to ${\mathrm{T}}_2$ is proportional to $({\mathrm{T}}_2-{\mathrm{T}}_1)$. Choose the correct answer from the options given below :

1. A.(B), (D) only
2. B.(B), (E) only
3. C.(A), (C), (E) only
4. D.(A), (C), (D) only

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, $\mathrm{PV}=\mathrm{constant}$, while in adiabatic process $P{V}^{\gamma }=\mathrm{constant}$. 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:

1. A.(A) is true but (R) is false
2. B.Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
3. C.(A) is false but (R) is true
4. D.Both (A) and (R) are true and (R) is the correct explanation of (A)

1. A.$500\mathrm{R}(\ln 3+\ln 4)$
2. B.$450\mathrm{R}(\ln 4-\ln 3)$
3. C.$500\mathrm{R}\ln 2$
4. D.$400\mathrm{R}\ln 4$

A Carnot engine ($\mathrm{E}$) is working between two temperatures $473\mathrm{K}$ and $273\mathrm{K}$ . In a new system two engines - engine $E_1$ works between $473\mathrm{K}$ to $373\mathrm{K}$ and engine $E_2$ works between $373\mathrm{K}$ to $273\mathrm{K}$ . If ${\eta }_{12},{\eta }_1$ and ${\eta }_2$ are the efficiencies of the engines $E,E_1$ and $E_2$, respectively, then

1. A.${\eta }_{12}={\eta }_1{\eta }_2$
2. B.${\eta }_{12}={\eta }_1+{\eta }_2$
3. C.${\eta }_{12}\ge {\eta }_1+{\eta }_2$
4. D.${\eta }_{12}<{\eta }_1+{\eta }_2$

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:

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

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 :

1. A.Both (A) and (R) are true and (R) is the correct explanation of (A)
2. B.Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
3. C.(A) is false but (R) is true
4. D.(A) is true but (R) is false

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 :

1. A.$\mathrm{m}({\mathrm{T}}_2-{\mathrm{T}}_1)$
2. B.zero
3. C.$\mathrm{m}\ln \left(\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}\right)$
4. D.$\mathrm{m}\ln \left(\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}\right)$

An amount of ice of mass $10^{-3}\text{ kg}$ and temperature $-10^{\circ }\mathrm{C}$ is transformed to vapour of temperature $110^{\circ }\mathrm{C}$ by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice $=2100{\text{ J kg}}^{-1}{\text{ K}}^{-1}$, specific heat of water $=4180{\text{ J kg}}^{-1}{\text{ K}}^{-1}$, specific heat of steam $=1920{\text{ J kg}}^{-1}{\text{ K}}^{-1}$, Latent heat of ice $=3.35\times 10^5{\text{ J kg}}^{-1}$ and Latent heat of steam $=2.25\times 10^6{\text{ J kg}}^{-1}$ )

1. A.$3022\text{ J}$
2. B.$3043\text{ J}$
3. C.$3003\text{ J}$
4. D.$3024\text{ J}$

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.$\frac{16}{25}$

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.$\frac{T}{\mathrm{R}}[2+\sqrt{2}]$

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.$\frac{5}{3}$

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.$\frac{V_a}{V_d}={\left(\frac{V_b}{V_c}\right)}^2$

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.$250\mathrm{J}$

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.$\frac{9}{7}$

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.$RT[\sqrt{2}-2]$

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.$\frac{9}{4}\mathrm{R}$

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.$850\text{ J}$

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 $x=$ ________ .

1. A.$P_2>P_1$
2. B.$P_1>P_2$
3. C.$P_1=P_2$
4. D.$P_2\ge P_1$

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