Question

The process AB is shown in the diagram. As the gas is taken from A to B, its internal energy

• A. initially increases then decreases.
• B. initially decreases then increases.
• C. remains constant.
• D. variation depends on type of gas.

Answer 1

Answer: (A)

initially increases then decreases.

Let us first find the equation of the straight line,

$\frac{P-2p}{V-v}=\frac{2p-p}{v-2v}$

$P-2p=V\times \left(\frac{-p}{v}\right)$

$\therefore$ equation of the line : $P=V\times \left(\frac{-p}{v}\right)+2p$

We know that internal Energy $\left(U\right)=PV$

$U=P\times V=V\times (V\times (\frac{-p}{v})+2p)$
$U=-V^2\times \left(\frac{p}{v}\right)+2pV$
As we go from point A to point B volume increases .
As volume increases internal energy initially increases and then decreases, since the internal energy as a function of volume is a downward parabola.