 JEE Mains Previous Years Questions with Solutions

4.5
star star star star star
1

AIEEE 2009

Two moles of helium gas are taken over the cycle $ABCD$, as shown in the $P$-$T$ diagram. The net work done on the gas in the cycle $ABCDA$ is:

A
$276$ $R$
B
$1076$ $R$
C
$1904$ $R$
D
zero

Explanation

The net work in the cycle $ABCD$ is
$W = {W_{AB}} + {W_{BC}} + {W_{CD}} + {W_{DA}}$
$= 400R + 2.303nRT\log {{{P_B}} \over {{P_C}}} + \left( { - 400R} \right) - 414R$
$= 2.303 \times 2R \times 500\log {{2 \times {{10}^5}} \over {1 \times {{10}^5}}} - 414R$
$= 693.2\,R - 414\,R = 279.2\,R$
2

AIEEE 2009

Two moles of helium gas are taken over the cycle $ABCD,$ as shown in the $P$-$T$ diagram. The work done on the gas in taking it from $D$ to $A$ is :

A
$+414$ $R$
B
$-690$ $R$
C
$+690$ $R$
D
$-414$ $R$

Explanation

Work done by the system in the isothermal process
$DA$ is $W = 2.303nRT\,{\log _{10}}{{{P_D}} \over {{P_A}}}$
$= 2.303 \times 2R \times 300{\log _{10}}{{1 \times {{10}^5}} \over {2 \times {{10}^5}}} = - 414R.$
Therefore work done on the gas is $+ \,414\,R.$
3

AIEEE 2009

Two moles of helium gas are taken over the cycle $ABCD,$ as shown in the $P$-$T$ diagram. Assuming the gas to be ideal the work done on the gas in taking it from $A$ to $B$ is :

A
$300$ $R$
B
$400$ $R$
C
$500$ $R$
D
$200$ $R$

Explanation

$A$ to $B$ is an isobaric process. The work done
$W = nR\left( {{T_2} - {T_1}} \right) = 2R\left( {500 - 300} \right) = 400R$
4

AIEEE 2009

A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta$ along the length $x$ of the bar from its hot end is best described by which of the following figures?
A B C D Explanation

The heat flow rate is given by

${{dQ} \over {dt}} = {{kA\left( {{\theta _1} - \theta } \right)} \over x}$

$\Rightarrow {\theta _1} - \theta$ $= {x \over {kA}}{{dQ} \over {dt}}$

$\Rightarrow \theta$ $= {\theta _1} - {x \over {kA}}{{dQ} \over {dt}}$

where ${\theta _1}$ is the temperature of hot end and $\theta$ is temperature at a distance $x$ from hot end.
The above equation can be graphically represented by option $(a).$