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1

AIEEE 2006

MCQ (Single Correct Answer)
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 $${N_2}$$
$${n_1}C{v_1}\Delta {T_1} = {n_2}C{v_2}\Delta {T_2}$$
$${3 \over 2}R\left[ {{7 \over 3}{T_0} - {T_f}} \right]$$
$$ = {5 \over 2}R\left[ {{T_f} - {T_0}} \right] \Rightarrow {T_f}$$
$$ = {3 \over 2}{T_0}$$
2

AIEEE 2006

MCQ (Single Correct Answer)
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 $$ = {{\sigma {T^4}{R^2}} \over {{r^2}}}\left( {\pi r_0^2} \right)$$
3

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.
4

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 $${Q_3} = 0$$
$$\eta = 1 - {{{Q_2}} \over {{Q_1}}} = 1 - {{{T_0}{S_0}} \over {{3 \over 2}{T_0}{S_0}}} = {1 \over 3}$$

Questions Asked from Heat and Thermodynamics

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