Heat & Thermodynamics · JEE Advanced previous year questions

The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of $1000\mathrm{K}$ is $0.4$. It extracts $150\mathrm{J}$ of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump which has a coefficient of performance $10$. The hot reservoir of the heat pump is at a temperature of $300\mathrm{K}$. Which of the following statements is/are correct:

1. A.Work extracted from the Carnot engine in one cycle is $60\mathrm{J}$.
2. B.Temperature of the cold reservoir of the Carnot engine is $600\mathrm{K}$.
3. C.Temperature of the cold reservoir of the heat pump is $270\mathrm{K}$.
4. D.Heat supplied to the hot reservoir of the heat pump in one cycle is $540\mathrm{J}$.

One mole of an ideal gas expands adiabatically from an initial state $(T_A,V_0)$ to final state $(T_f,5V_0)$. Another mole of the same gas expands isothermally from a different initial state $(T_B,V_0)$ to the same final state $(T_f,5V_0)$. The ratio of the specific heats at constant pressure and constant volume of this ideal gas is $\gamma$. What is the ratio $T_A/T_B$?

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

A closed container contains a homogeneous mixture of two moles of an ideal monatomic gas ($\gamma =5/3$) and one mole of an ideal diatomic gas ($\gamma =7/5$). Here, $\gamma$ is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mixture does a work of $66\mathrm{Joule}$ when heated at constant pressure. The change in its internal energy is ____ Joule.

Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option. [Given: Wien's constant as $2.9\times 10^{-3}\mathrm{m}\text{-}\mathrm{K}$ and $\frac{hc}{e}=1.24\times 10^{-6}\mathrm{V}\text{-}\mathrm{m}$] $$\begin{array}{ll}\text{List-I}& \text{List-II}\\ \text{(P) }2000\mathrm{K}& \text{(1) The radiation at peak wavelength can lead to emission of photoelectrons from a metal of work function }4\mathrm{eV}.\\ \text{(Q) }3000\mathrm{K}& \text{(2) The radiation at peak wavelength is visible to human eye.}\\ \text{(R) }5000\mathrm{K}& \text{(3) The radiation at peak emission wavelength will result in the widest central maximum of a single slit diffraction.}\\ \text{(S) }10000\mathrm{K}& \text{(4) The power emitted per unit area is }1/16\text{ of that emitted by a blackbody at temperature }6000\mathrm{K}.\\ & \text{(5) The radiation at peak emission wavelength can be used to image human bones.}\end{array}$$

1. A.$P\to 3,Q\to 5,R\to 2,S\to 3$
2. B.$P\to 3,Q\to 2,R\to 4,S\to 1$
3. C.$P\to 3,Q\to 4,R\to 2,S\to 1$
4. D.$P\to 1,Q\to 2,R\to 5,S\to 3$