### JEE Mains Previous Years Questions with Solutions

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1

### AIEEE 2007

A Carnot engine, having an efficiency of $\eta = 1/10$ as heat engine, is used as a refrigerator . If the work done on the system is $10$ $J$, the amount of energy absorbed from the reservoir at lower temperature is
A
$100$ $J$
B
$99$ $J$
C
$90$ $J$
D
$1$ $J$

## Explanation

The efficiency $\left( \eta \right)$ of a Carnot engine and the coefficient of performance $\left( \beta \right)$ of a refrigerator are related as
$\beta = {{1 - \eta } \over \eta }$
$\,\,\,\,\,\,$ Here, $\eta = {1 \over {10}}$
$\,\,\,\,\,\,$ $\therefore$ $\beta = {{1 - {1 \over {10}}} \over {\left( {{1 \over {10}}} \right)}} = 9.$

Also, Coefficient of performance $\left( \beta \right)$ is given by $\beta = {{{Q_2}} \over W},$
where ${Q_2}$ is the energy absorbed from the reservoir.
or, $9 = {{{Q_2}} \over {10}}$
$\therefore$ ${Q_2} = 90\,J.$

2

### AIEEE 2006

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature ${T_0},$ while Box contains one mole of helium at temperature $\left( {{7 \over 3}} \right){T_0}.$ The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases, ${T_f}$ in terms of ${T_0}$ is
A
${T_f} = {3 \over 7}{T_0}$
B
${T_f} = {7 \over 3}{T_0}$
C
${T_f} = {3 \over 2}{T_0}$
D
${T_f} = {5 \over 2}{T_0}$

## Explanation

Heat lost by He $=$ Heat gained by ${N_2}$
${n_1}C{v_1}\Delta {T_1} = {n_2}C{v_2}\Delta {T_2}$
${3 \over 2}R\left[ {{7 \over 3}{T_0} - {T_f}} \right]$
$= {5 \over 2}R\left[ {{T_f} - {T_0}} \right] \Rightarrow {T_f}$
$= {3 \over 2}{T_0}$
3

### AIEEE 2006

Assuming the Sun to be a spherical body of radius $R$ at a temperature of $TK$, evaluate the total radiant powered incident of Earth at a distance $r$ from the Sun

Where r0 is the radius of the Earth and $\sigma$ is Stefan's constant.

A
$4\pi r_0^2{R^2}\sigma {{{T^4}} \over {{r^2}}}$
B
$\pi r_0^2{R^2}\sigma {{{T^4}} \over {{r^2}}}$
C
$r_0^2{R^2}\sigma {{{T^4}} \over {4\pi {r^2}}}$
D
${R^2}\sigma {{{T^4}} \over {{r^2}}}$

## Explanation

Total power radiated by Sun $= \sigma {T^4} \times 4\pi {R^2}$

The intensity of power at earth's surface $= {{\sigma {T^4} \times 4\pi {R^2}} \over {4\pi {r^2}}}$

Total power received by Earth $= {{\sigma {T^4}{R^2}} \over {{r^2}}}\left( {\pi r_0^2} \right)$
4

### AIEEE 2006

The work of $146$ $kJ$ 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 $\left( {R = 8.3J\,\,mo{l^{ - 1}}\,{K^{ - 1}}} \right)$
A
diatomic
B
triatomic
C
a mixture of monoatomic and diatomic
D
monoatomic

## Explanation

$W = {{nR\Delta T} \over {1 - \gamma }} \Rightarrow - 146000$
$= {{1000 \times 8.3 \times 7} \over {1 - \gamma }}$
or $1 - \gamma = - {{58.1} \over {146}} \Rightarrow \gamma$
$= 1 + {{58.1} \over {146}} = 1.4$
Hence the gas is diatomic.