$A$ Carnot cycle consists of

The efficiency of a Carnot engine which operates between the two temperatures $T_1 = 500 \text{ K}$ (source) and $T_2 = 300 \text{ K}$ (sink) is: (in $\%$)

$A$ Carnot engine operating between temperatures $T_1$ and $T_2$ has an efficiency of $\frac{1}{6}$. When $T_2$ is lowered by $62\, K$,its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ are,respectively:

$300 \, cal$ of heat is given to a heat engine and it rejects $225 \, cal$ of heat. If the source temperature is $227^{\circ} C$,then the temperature of the sink will be . . . . . . $^{\circ} C$.

Efficiency 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 $\,K$)

$A$ Carnot engine has the same efficiency between $800 \ K$ and $500 \ K$ and between $x \ K$ and $600 \ K$. The value of '$x$' is: (in $K$)