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JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2006

MCQ (Single Correct Answer)
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.
2

AIEEE 2005

MCQ (Single Correct Answer)
The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is
A
$${1 \over 4}$$
B
$${1 \over 2}$$
C
$${2 \over 3}$$
D
$${1 \over 3}$$

Explanation


$${Q_1} = {T_0}{S_0} + {1 \over 2}{T_0}{S_0} = {3 \over 2}{T_0}{S_0}$$
$${Q_2} = {T_0}\left( {2{S_0} - {S_0}} \right)$$ $$ = {T_0}{S_0}$$
and $${Q_3} = 0$$
$$\eta = 1 - {{{Q_2}} \over {{Q_1}}} = 1 - {{{T_0}{S_0}} \over {{3 \over 2}{T_0}{S_0}}} = {1 \over 3}$$
3

AIEEE 2005

MCQ (Single Correct Answer)
The figure shows a system of two concentric spheres of radii $${r_1}$$ and $${r_2}$$ are kept at temperatures $${T_1}$$ and $${T_2}$$, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to
A
$$In\left( {{{{r_2}} \over {{r_1}}}} \right)$$
B
$${{\left( {{r_2} - {r_1}} \right)} \over {\left( {{r_1}{r_2}} \right)}}$$
C
$${\left( {{r_2} - {r_1}} \right)}$$
D
$${{{r_1}{r_2}} \over {\left( {{r_2} - {r_1}} \right)}}$$

Explanation


Consider a shell of thickness $$(dr)$$ and of radius $$(r)$$ and the temperature of inner and outer surfaces of this shell be $$T,(T-dT)$$
$$H = {{KA\left[ {\left( {T - dT} \right) - T} \right]} \over {dr}} = {{ - KAdT} \over {dr}}$$
$$H = - 4\pi K{r^2}{{dT} \over {dr}}$$ ( as $$A = 4\pi {r^2}$$ )
Then, $$\left( H \right)\int\limits_{{r_1}}^{{r^2}} {{1 \over {{r^2}}}} dr = - 4\pi K\int\limits_{{T_1}}^{{T_2}} {dT} $$
$$H\left[ {{1 \over {{r_1}}} - {1 \over {{r_2}}}} \right] = - 4\pi K\left[ {{T_2} - {T_1}} \right]$$
or $$H = {{ - 4\pi K{r_1}{r_2}\left( {{T_2} - {T_1}} \right)} \over {\left( {{r_2} - {r_1}} \right)}}$$
4

AIEEE 2005

MCQ (Single Correct Answer)
A system goes from $$A$$ to $$B$$ via two processes $$I$$ and $$II$$ as shown in figure. If $$\Delta {U_1}$$ and $$\Delta {U_2}$$ are the changes in internal energies in the processes $$I$$ and $$II$$ respectively, then
A
relation between $$\Delta {U_1}$$ and $$\Delta {U_2}$$ can not be determined
B
$$\Delta {U_1} = \Delta {U_2}$$
C
$$\Delta {U_2} < \Delta {U_1}$$
D
$$\Delta {U_2} > \Delta {U_1}$$

Explanation

Change in internal energy do not depend upon the path followed by the process. It only depends on initial and final states $$i.e.,$$ $$\Delta U{}_1 = \Delta {U_2}$$

Questions Asked from Heat and Thermodynamics

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