(A) For a heat engine,the efficiency $\eta$ is defined as the ratio of work done to the heat absorbed from the source: $\eta = \frac{W}{Q_1} = \frac{Q

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(A) For a heat engine,the efficiency $\eta$ is defined as the ratio of work done to the heat absorbed from the source: $\eta = \frac{W}{Q_1} = \frac{Q_1 - Q_2}{Q_1}$.For a Carnot engine,this is also expressed in terms of temperatures as $\eta = \frac{T_1 - T_2}{T_1}$. Thus,$(a)$ matches with $(ii)$ and $(iii)$.For a heat pump,the coefficient of performance $(COP)$ is defined as the ratio of heat extracted from the cold reservoir to the work done: $\text{COP} = \frac{Q_2}{W} = \frac{Q_2}{Q_1 - Q_2}$. Thus,$(b)$ matches with $(i)$.Therefore,the correct matching is $(a-ii, iii)$ and $(b-i)$.

Class 11 Physics Thermodynamics Mix Examples-Thermodynamics

Medium

Match the devices in Column-$I$ with their efficiency/coefficient of performance in Column-$II$:

Column-$I$ Column-$II$

$(a)$ Heat engine $(i)$ $\text{COP} = \frac{Q_2}{Q_1 - Q_2}$

$(b)$ Heat pump $(ii)$ $\eta = \frac{Q_1 - Q_2}{Q_1}$

$(iii)$ $\eta = \frac{T_1 - T_2}{T_1}$

Column-$I$	Column-$II$
$(a)$ Heat engine	$(i)$ $\text{COP} = \frac{Q_2}{Q_1 - Q_2}$
$(b)$ Heat pump	$(ii)$ $\eta = \frac{Q_1 - Q_2}{Q_1}$
	$(iii)$ $\eta = \frac{T_1 - T_2}{T_1}$

A
$(a-ii, iii), (b-i)$
B
$(a-ii), (b-i, iii)$
C
$(a-i), (b-ii, iii)$
D
$(a-i, ii), (b-iii)$

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When a system is taken from state $i$ to state $f$ along the path $iaf$,$Q = 50 \ J$ and $W = 20 \ J$. Along the path $ibf$,$Q = 35 \ J$ and $W = -13 \ J$. For the curved path $fi$,$Q = \dots \ J$.

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EasyAP EAMCET 2019

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Match the devices in Column-$I$ with their efficiency/coefficient of performance in Column-$II$: Column-$I$ Column-$II$ $(a)$ Heat engine $(i)$ $\text{COP} = \frac{Q_2}{Q_1 - Q_2}$ $(b)$ Heat pump $(ii)$ $\eta = \frac{Q_1 - Q_2}{Q_1}$ $(iii)$ $\eta = \frac{T_1 - T_2}{T_1}$

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When a system is taken from state $i$ to state $f$ along the path $iaf$,$Q = 50 \ J$ and $W = 20 \ J$. Along the path $ibf$,$Q = 35 \ J$ and $W = -13 \ J$. For the curved path $fi$,$Q = \dots \ J$.

$A$ monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in increasing the internal energy and that used for doing external work is $A$ and $B$ respectively. Then the ratio,$A: B$ is

$A$ gas expands with temperature according to the relation,$V=k T^{2/3}$,where $k$ is a constant. Work done when the temperature changes by $60 \ K$ is ($R=$ universal gas constant.) (in $R$)

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Match the devices in Column-$I$ with their efficiency/coefficient of performance in Column-$II$:

Column-$I$ Column-$II$

$(a)$ Heat engine $(i)$ $\text{COP} = \frac{Q_2}{Q_1 - Q_2}$

$(b)$ Heat pump $(ii)$ $\eta = \frac{Q_1 - Q_2}{Q_1}$

$(iii)$ $\eta = \frac{T_1 - T_2}{T_1}$