### JEE Mains Previous Years Questions with Solutions

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1

### AIEEE 2003

According to Newton's law of cooling, the rate of cooling of a body is proportional to ${\left( {\Delta \theta } \right)^n},$ where ${\Delta \theta }$ is the difference of the temperature of the body and the surrounding, and $n$ is equal to
A
two
B
three
C
four
D
one

## Explanation

$- {{dQ} \over {dt}} \propto \left( {\Delta \theta } \right)$
2

### AIEEE 2003

A carnot engine takes $3 \times {10^6}$ cal. of heat from a reservoir at ${627^ \circ }C,$ and gives it to a sink at ${27^ \circ }C$. The work done by the engine is
A
$4.2 \times {10^6}J$
B
$8.4 \times {10^6}J$
C
$16.8 \times {10^6}J$
D
zero

## Explanation

$\eta = 1 - {{{T_2}} \over {{T_1}}}$

$= 1 - {{\left( {273 + 27} \right)} \over {\left( {273 + 627} \right)}}$

$= 1 - {{300} \over {900}}$

$= 1 - {1 \over 3} = {2 \over 3}$

But $\eta = {W \over Q}$

$\therefore$ ${W \over Q} = {2 \over 3} \Rightarrow W$

$= {2 \over 3} \times Q$

$= {2 \over 3} \times 3 \times {10^6}$

$= 2 \times {10^6}cal$

$= 2 \times {10^6} \times 4.2\,J$

$= 8.4 \times {10^6}J$
3

### AIEEE 2003

Which of the following parameters does not characterize the thermodynamic state of mattter?
A
Temperature
B
Pressure
C
Work
D
Volume

## Explanation

Work is a path function. The remaining three parameters are state function.
4

### AIEEE 2003

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio ${C_p}/{C_V}$ for the gas is
A
${4 \over 3}$
B
$2$
C
${5 \over 3}$
D
${3 \over 2}$

## Explanation

$P \propto {T^3} \Rightarrow P{T^{ - 3}} =$ constant ....$(i)$
But for an adiabatic process, the pressure temperature relationship is given by
${P^{1 - \gamma }}\,\,{T^\gamma } =$ constant $\Rightarrow P{T^{{\gamma \over {1 - \gamma }}}} =$ constant. ....$(ii)$
From $(i)$ and $(ii)$ ${\gamma \over {1 - \gamma }} = - 3 \Rightarrow \gamma = - 3 + 3\gamma \Rightarrow \gamma = {3 \over 2}$