Question

One mole of an ideal monoatomic gas expands tillits

Answer 1

One mole of an ideal gas at temperature T1 expands according to the law P/V^2 = a (constant). What is the work done by the gas until the temperature of the gas becomes T2?

Let us use the definition of work to calculate the work done by the gas

Wgas=∫V2V1P.dv

Since P=aV2,

Wgas=∫V2V1aV2.dv

=a(V23−V13)3

But we need to find work in terms of T1 and T2

From Ideal Gas equation, we have PV=nRT

Therefore P=nRTV

Put this in the P=aV2,

Therefore, nRTV=aV2

or V3=nRTa

Since n=1,

V3=RTa

Now substitute this in the expression of work Wgas=a(V23−V13)3

Therefore Wgas=aR(T2−T1)3a

=R(T2−T1)3

Hope this helps ;)