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Question

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

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Solution

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.

Clearly the volume has become doubled.

Thus the density=mV becomes half of initial value.

For an ideal gas, PV=nRT

⟹T∝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, PV=k

⟹P=kV

Using the relation in ideal gas equation gives,

(kV)V=nRT

⟹kV2=nRT

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

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