$1m^3=1,000L$

Carnot cycle

A Carnot cycle $($shown in the diagram on the right$)$ consists of two isothermal processes connected via two adiabatic processes.

Our goal is to fisure out the efficiency for this cycle:

$e=\frac{W_{by}\text{g}\text{a}\text{s}}{Q_h}$

$W_{by\text{g}\text{a}\text{s}}$ is the work done by the gas in one cycle

$Q_h$ is the heat that was added to the gas in one cycle.

We will do this by considering a specific case.

Problem we will solve:

Suppose the gas being used in a Carnot cycle is ideal diatomic with $C_V=\frac{5}{2}R.$ The following are known:

Point A: $P_A=15$atm;$V_A=1\mathrm{.}0L$;$T_A=450K.$

Point B: $V_B=1\mathrm{.}5L$

Point C: $V_C=3\mathrm{.}0L$

Point D: $V_D=2\mathrm{.}0L$

Part $1$: Calculating pressure, volume, and temperature at each point in the cycle.

A$.$ To make it easy to keep track of things, we will fill out a table with the pressure, volume, and temperature each point. In the table below, add the values given in the text of the problem. As you figure out the oth values, add them to the table. In all calculations, use three significant figures.

$\backslash$table$[[,$Pressure $($atm$),$Volume $($L$),$Temperature $($K$)],[$Point A$,,,],[$Point B$,,,],[$Point C$,,,],[$Point D$,,,]]$