$A$ Carnot engine works between $27^{\circ} C$ and $127^{\circ} C$. Heat supplied by the source is $500 \ J$. The heat ejected to the sink is (in $J$):

The efficiency of a Carnot engine is $\eta$ when its hot and cold reservoirs are maintained at temperatures $T_1$ and $T_2$, respectively. To increase the efficiency to $1.5 \eta$, the increase in temperature $(\Delta T)$ of the hot reservoir, while keeping the cold reservoir constant at $T_2$, is

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1 :$ An inventor claims to have constructed an engine that has an efficiency of $30\%$ when operated between the boiling and freezing points of water. This is not possible.
Statement $2:$ The efficiency of a real engine is always less than the efficiency of a Carnot engine operating between the same two temperatures.

An engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62^{\circ}C$,its efficiency is doubled. The temperature of the source is ....... $^{\circ}C$.

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.

What is a Carnot cycle? Explain it by drawing a figure.