In a Carnot engine,if the work done during isothermal expansion is $25 \%$ more than the work done during isothermal compression,then the efficiency of the engine is: (in $\%$)

$A$ Carnot engine operates between two reservoirs of temperatures $900 \; K$ and $300 \; K$. The engine performs $1200 \; J$ of work per cycle. The heat energy (in $J$) delivered by the engine to the low-temperature reservoir in a cycle is:

Two Carnot engines $A$ and $B$ operate in series such that engine $A$ absorbs heat $Q_1$ at temperature $T_1$ and rejects heat $Q$ to a sink at temperature $T$. Engine $B$ absorbs half of the heat rejected by engine $A$ (i.e.,$Q/2$) and rejects heat $Q_3$ to the sink at temperature $T_3$. When the work done in both cases is equal,the value of $T$ is:

Show the four steps of a Carnot engine in a $P-V$ graph,write the equation for each step,and obtain the work done by the system. Also,derive the efficiency of a Carnot engine.

An engine operating between temperatures $T_1$ and $T_2$ has efficiency $\eta = \frac{1}{5}$. When $T_2$ is lowered by $45 \ K$,its efficiency becomes $\eta' = \frac{1}{2}$. Temperatures $T_1$ and $T_2$ are respectively:

$A$ Carnot engine whose low temperature reservoir is at $7\,^{\circ}C$ has an efficiency of $50\%$. It is desired to increase the efficiency to $70\%$. By how many degrees should the temperature of the high temperature reservoir be increased? (in $K$)