The temperature of food material in a refrigerator is $4^{\circ} C$ and the temperature of the environment is $15^{\circ} C$. If a Carnot cycle is used in its working gas,find its Carnot efficiency.

$A$ Carnot engine whose sink is at $300 \, K$ has an efficiency of $50 \%$. By how much should the temperature of the source be increased so that the efficiency becomes $70 \%$?

The efficiency of a Carnot cycle is $\frac{1}{6}$. By lowering the temperature of the sink by $65 \ K$,it increases to $\frac{1}{3}$. The initial and final temperatures of the sink are:

The Carnot cycle (reversible) of a gas represented by a Pressure-Volume $(P-V)$ curve is shown in the diagram. Consider the following statements:
$I.$ Area $ABCD =$ Work done by the gas
$II.$ Area $ABCD =$ Net heat absorbed
$III.$ Change in the internal energy in the cycle $= 0$
Which of these are correct?

What is the source temperature of the Carnot engine required to get $70 \%$ efficiency (in $^{\circ}C$)? Given sink temperature $= 27^{\circ}C$.

$A$ reversible Carnot heat engine converts $\frac{1}{4}$ of its input heat into work. When the temperature of the sink is reduced by $50 \ K$,its efficiency becomes $33 \frac{1}{3} \%$. The initial temperatures of the source and the sink respectively are