91Ó°ÊÓ

• Isothermal expansion$\text{W}=40\text{ J}$
• Adiabatic expansion,$\text{W}=20\text{ J}$
• Isothermal expansion,$\text{W}=30\text{J}$

The expression for the heat from the first law of thermodynamics is given by,

$Q=W+\mathrm{Δ}U$

Here Q is the heat required, W is the work done, $\mathrm{Δ}U$is the change in internal energy.

So, the first law of thermodynamics gives the relation between heat, work and internal energy.

For path 1:

As internal energy is a state function for an isothermal process,$dU=0$.

For adiabatic process,$dQ=0$,

Therefore,$\text{d}U=-dW$

Therefore, net change in internal energy of path 1 is

$dU=−20\text{ J}$

But, internal energy is independent of the path, so change in internal energy along path 2 is the same as path 1.

$dU=−20\text{ J}$

Therefore the change in internal energy along path 2 is$−20\text{ J}$ .