$A$ Carnot engine with sink's temperature at $17\,^{\circ}C$ has $50\%$ efficiency. By how much should its source temperature be changed to increase its efficiency to $60\%$? (in $K$)

$A$ diatomic ideal gas is used in a Carnot engine as a working substance. If during the adiabatic expansion part of the cycle,the volume of the gas increases from $V$ to $32V$,the efficiency of the engine is:

$A$ Carnot engine $A$ working between temperatures $600 \ K$ and $T$ $(T < 600 \ K)$ and another Carnot engine $B$ working between temperatures $T$ $(T > 400 \ K)$ and $400 \ K$ are connected in series. If the work done by both the engines is the same, then $T =$ (in $K$)

$A$ diatomic ideal gas is used in a Carnot engine as the working substance. During the adiabatic expansion of the cycle,if the volume of the gas increases from $V$ to $32 V$,then the efficiency of the engine is

In the $1^{\text{st}}$ case,a Carnot engine operates between temperatures $300 \, K$ and $100 \, K$. In the $2^{\text{nd}}$ case,as shown in the figure,a combination of two engines is used. The efficiency of this combination (in the $2^{\text{nd}}$ case) will be:

What is the efficiency of a heat engine? Write its formula.