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1

AIEEE 2007

MCQ (Single Correct Answer)
When a system is taken from state $$i$$ to state $$f$$ along the path iaf, it is found that $$Q=50$$ cal and $$W=20$$ $$cal$$. Along the path $$ibf$$ $$Q=36$$ $$cal.$$ $$W$$ along the path $$ibf$$ is
A
$$14$$ $$cal$$
B
$$6$$ $$cal$$
C
$$16$$ $$cal$$
D
$$66$$ $$cal$$

Explanation

For path iaf, $$\Delta U = Q - W = 50 - 20 = 30\,cal.$$
For path ibf, $$W = Q - \Delta U = 36 - 30 = 6\,cal.$$
2

AIEEE 2007

MCQ (Single Correct Answer)
If $${C_p}$$ and $${C_v}$$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then
A
$${C_p} - {C_v} = 28R$$
B
$${C_p} - {C_v} = R/28$$
C
$${C_p} - {C_v} = R/14$$
D
$${C_p} - {C_v} = R$$

Explanation

According to Mayer's relationship $${C_p} - {C_v} = R$$
$$\therefore$$ $${{{C_p}} \over M} - {{{C_v}} \over M} = {R \over M}$$ $$\,\,\,\,\,\,$$ Here $$M=28.$$
3

AIEEE 2007

MCQ (Single Correct Answer)
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, $$9 = {{{Q_2}} \over {10}}$$
$$\therefore$$ $${Q_2} = 90\,J.$$

4

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

Questions Asked from Heat and Thermodynamics

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