State Carnot's theorem.
(N/A) Carnot's theorem states two main points regarding the efficiency of heat engines:
$1$. All reversible heat engines operating between the same two temperatures ($T_1$ and $T_2$) have the same efficiency,regardless of the working substance used.
$2$. No irreversible heat engine operating between two given temperatures can have an efficiency greater than that of a reversible heat engine operating between the same two temperatures.
Mathematically,the efficiency $\eta$ of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$,where $T_1$ is the temperature of the source and $T_2$ is the temperature of the sink.
$1$. All reversible heat engines operating between the same two temperatures ($T_1$ and $T_2$) have the same efficiency,regardless of the working substance used.
$2$. No irreversible heat engine operating between two given temperatures can have an efficiency greater than that of a reversible heat engine operating between the same two temperatures.
Mathematically,the efficiency $\eta$ of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$,where $T_1$ is the temperature of the source and $T_2$ is the temperature of the sink.
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For an ideal heat engine,the temperature of the source is $127\,^{\circ} C$. In order to have $60\, \%$ efficiency,the temperature of the sink should be $........\,{ }^{\circ} C$. (Round off to the nearest integer)
$A$ Carnot engine operating between temperatures $600 \,K$ and $300 \,K$ absorbs $800 \,J$ of heat from the source. The mechanical work done per cycle is (in $\,J$)
$A$ Carnot engine has an efficiency of $40\%$. The temperature of its sink is $300 \ K$. To increase the efficiency by $50\%$ of its original efficiency while keeping the sink temperature constant,by how many $K$ must the source temperature be increased?
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View SolutionThree Carnot engines operate in series between a heat source at temperature $T_1$ and a heat sink at a temperature $T_4$. There are two other reservoirs at temperatures $T_2$ and $T_3$. If the three engines are equally efficient,find the values of $T_2$ and $T_3$ in terms of $T_1$ and $T_4$,given that $T_1 > T_2 > T_3 > T_4$.
DifficultAP EAMCET 2021
View SolutionEfficiency of a heat engine whose sink is at temperature of $300 \,K$ is $40 \%$. To increase the efficiency to $60 \%$, keeping the sink temperature constant, the source temperature must be increased by (in $\,K$)
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