$A$ Carnot engine operating between temperatures $7^{\circ}C$ and a higher temperature has an efficiency of $50\%$. To increase its efficiency to $70\%$,by how much must the temperature of the source be increased in $K$?

Consider a two-stage Carnot engine. In the first stage,heat $Q_1$ is absorbed at temperature $T$ and heat $Q_2$ is expelled at temperature $\alpha T$ (where $\alpha < 1$). In the second stage,heat $Q_2$ is absorbed at temperature $\alpha T$ and heat $Q_3$ is expelled at temperature $\beta T$ (where $\beta < \alpha$). The efficiency of the Carnot engine will be

$A$ scientist claims that the efficiency of their heat engine,which operates between a source temperature of $127^{\circ}C$ and a sink temperature of $27^{\circ}C$,is $26\%$. Then:

$A$ Carnot heat engine has an efficiency of $50 \%$. The temperature of the sink is maintained at $500 \ K$. To increase the efficiency up to $80 \%$,the required increment in the source temperature is: (in $K$)

$A$ Carnot engine operates between a source and a sink. The efficiency of the engine is $40 \%$ and the temperature of the sink is $27^{\circ} C$. If the efficiency is to be increased to $50 \%$,then the temperature of the source must be increased by: (in $K$)

The efficiency of a Carnot heat engine: