Determine the efficiency of a Carnot cycle if,in the adiabatic expansion,the volume becomes $3$ times its initial value and $\gamma = 1.5$.

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.

The efficiency of a Carnot heat engine is $0.5$ when the temperature of the source is $T_{1}$ and that of the sink is $T_{2}$. The efficiency of another Carnot heat engine is also $0.5$. The temperatures of the source and sink of the second engine are respectively:

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

Three designs are proposed for an engine which is to operate between $500 \ K$ and $300 \ K$. Design $A$ claims to produce $150 \ J$ of work per $1000 \ J$ of heat input, design $B$ $450 \ J$ of work per $1000 \ J$, and design $C$ $300 \ J$ of work per $1000 \ J$. Which of the designs would you choose?

Let $\eta_{1}$ be the efficiency of a Carnot engine at $T_{H}=447^{\circ}C$ and $T_{L}=147^{\circ}C$,while $\eta_{2}$ is the efficiency at $T_{H}=947^{\circ}C$ and $T_{L}=47^{\circ}C$. The ratio $\frac{\eta_{1}}{\eta_{2}}$ will be: