Question

In the P-V diagram shown in figure, choose the correct options for the process a - b

• A. density of gas reduced to half
• B. temperature of gas has increased to two times
• C. internal energy of gas has increased to four times
• D. T - V graphs is a pararabola passing through origin.

Answer 1

Answer: (A), (C), (D)

The correct options are
A density of gas reduced to half
C internal energy of gas has increased to four times
D T - V graphs is a pararabola passing through origin.

Clearly the volume has become doubled.

Thus the density$=\frac{m}{V}$ becomes half of initial value.

For an ideal gas, $PV=nRT$

$⟹T\propto PV$

Since both $P,V$ double, the T becomes four times. Internal energy is proportional to temperature of the gas. Thus it also becomes four times.

Since P-V curve has a constant slope, $\frac{P}{V}=k$

$⟹P=kV$

Using the relation in ideal gas equation gives,

$\left(kV\right)V=nRT$

$⟹k{V}^2=nRT$

Thus T-V graph is a parabola passing through origin.