(C) The efficiency of a Carnot engine is given by the formula: $\eta = 1 - \frac{T_2}{T_1}$.Here,the source temperature $T_1 = 411 + 273 = 684 \, K$ a

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(C) The efficiency of a Carnot engine is given by the formula: $\eta = 1 - \frac{T_2}{T_1}$.Here,the source temperature $T_1 = 411 + 273 = 684 \, K$ and the sink temperature $T_2 = 69 + 273 = 342 \, K$.Substituting these values into the efficiency formula: $\eta = 1 - \frac{342}{684} = 1 - 0.5 = 0.5$.The work done per cycle is equal to the area enclosed by the $PV$ diagram,which is given by $W = \eta \times Q$.Given that the heat extracted $Q = 1000 \, J$,we have $W = 0.5 \times 1000 = 500 \, J$.

Class 11 Physics Thermodynamics Heat Engine and Carnot Cycle

Medium

$A$ Carnot engine uses an ideal monoatomic gas first and then an ideal diatomic gas. If the source and sink temperatures are $411^{\circ}C$ and $69^{\circ}C$ respectively,and the engine extracts $1000 \, J$ of heat in each cycle,then the area enclosed by the $PV$ diagram is ........ $J$.

A
$100$
B
$300$
C
$500$
D
$700$

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Heat Engine and Carnot Cycle

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$A$ frictionless heat engine can be $100 \%$ efficient only if its exhaust temperature is ............

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$A$ Carnot engine operating between temperatures $T_1$ and $T_2$ has efficiency $\frac{1}{6}$. When $T_2$ is lowered by $60\,K$,its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ are respectively:

Difficult

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$A$ reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by $62^\circ C$,the efficiency of the engine is doubled. The temperatures of the source and sink are:

DifficultAIEEE 2011

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$A$ Carnot engine has an efficiency of $50 \%$. If the temperature of the sink is reduced by $40 \, K$,its efficiency increases by $30 \%$. The temperature of the source will be $.... \, K$.

MediumJEE MAIN 2022

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$A$ Carnot engine uses an ideal monoatomic gas first and then an ideal diatomic gas. If the source and sink temperatures are $411^{\circ}C$ and $69^{\circ}C$ respectively,and the engine extracts $1000 \, J$ of heat in each cycle,then the area enclosed by the $PV$ diagram is ........ $J$.

Similar Questions

$A$ car engine has a power of $20 kW$. The car makes a round trip of $1$ hour. If the thermal efficiency of the engine is $40 \%$ and the ambient temperature is $300 K$, the energy generated by fuel combustion is: (in $kJ$)

$A$ frictionless heat engine can be $100 \%$ efficient only if its exhaust temperature is ............

$A$ Carnot engine operating between temperatures $T_1$ and $T_2$ has efficiency $\frac{1}{6}$. When $T_2$ is lowered by $60\,K$,its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ are respectively:

$A$ reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by $62^\circ C$,the efficiency of the engine is doubled. The temperatures of the source and sink are:

$A$ Carnot engine has an efficiency of $50 \%$. If the temperature of the sink is reduced by $40 \, K$,its efficiency increases by $30 \%$. The temperature of the source will be $.... \, K$.

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