Thermodynamic Processes

Work Done In Different Processes

Work done by an enclosed gas on its surroundings is given by

W = $\int$p dV

For different types of processes, we have got different relations between p (Pressure) and V (Volume) and accordingly we have different expressions for work.

(a) Isochoric Process

Here, the volume is constant throughout and therefore the work done by the gas, irrespective of the manner in which pressure varies, is zero

W_isochoric = 0

(b) Isobaric Process

In this case, pressure of the gas remains constant throughout the process. Hence,

$\int$ pdV = p $\Delta$V

= n R$\Delta$T(n = number of moles)

($\Delta$ T= change in absolute temperature)

(C) Isothermal process

The temperature remains constant throughout the process.

Using ideal gas equation, we get,

p=$\frac{nRT}{V}$

Hence,

$\int pdV$ pdV = n RT $\underset{V_1}{\overset{V_2}{\int }}\frac{dV}{V}$= n RT $\ln \frac{V_2}{V_1}$

(d) Adiabatic Process:

pV^g = Constant = C (say)

$\therefore$ $p=C{V}^{-\gamma }$

$\therefore$ W = $\int pdV$ = $\underset{V_1}{\overset{V_2}{\int }}C{V}^{-\gamma }dV$

= $\frac{p_1{V}_1-p_2{V}_2}{\gamma -1}$= -nC_v(T₂ - T₁)

The work done by a gas can also be evaluated from the p-V diagram of the process.

Area enclosed by the curve in a p-V diagram = work done by the gas