$A$ 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:

$A$ Carnot engine whose heat sink is at $27\,^{\circ} C$ has an efficiency of $25 \%$. By how many degrees should the temperature of the source be changed to increase the efficiency by $100 \%$ of the original efficiency?

The efficiency of a Carnot engine is found to increase from $25 \%$ to $40 \%$ on increasing the temperature $(T_1)$ of the source alone by $100 \ K$. The temperature $(T_2)$ of the sink is given by: (in $K$)

Three 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 $T_1 > T_2 > T_3 > T_4$.

$A$ Carnot engine with efficiency $50 \%$ takes heat from a source at $600 \ K$. To increase the efficiency to $70 \%$,keeping the temperature of the sink same,the new temperature of the source will be (in $K$)

$A$ Carnot engine working between $300\, K$ and $600\, K$ has a work output of $800\, J$ per cycle. How much heat energy is supplied to the engine from the source in each cycle? .... $J$