$A$ 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:

Who first proposed (invented) the Carnot engine?

What is the theoretical efficiency of a heat engine?

An ideal Carnot heat engine has an efficiency of $30\%$. It absorbs heat from a hot reservoir at $727^{\circ}C$. The temperature of the cold reservoir is .... $^{\circ}C$.

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.

In a Carnot engine,the temperature of the reservoir is $527^{\circ} C$ and that of the sink is $200 \; K$. If the work done by the engine when it transfers heat from the reservoir to the sink is $12000 \; kJ$,the quantity of heat absorbed by the engine from the reservoir is $x \times 10^{6} \; J$. Find the value of $x$.