Question

In a container, two mole of a diatomic ideal gas is allowed to expand against 1 atm pressure and its volume changes from 2 litre to 5 litre isobarically. Calculate the change in internal energy (in atm L).

• A. 7.5
• B. 6.5
• C. 5
• D. 3

Answer 1

The correct option is A 7.5

Solution:- (A) $7.5$

$W=P\Delta V=nR\Delta T$

$\Rightarrow \Delta T=\frac{P\Delta V}{nR}$

Given that:-

$n=2\text{moles}$

$P=1atm$

$V_i=2L$

$V_f=5L$

$\Delta V=V_f-V_i=5-2=3L$

$\therefore \Delta T=\frac{1\times 3}{2R}=\frac{3}{2R}$

Now, as we know that,

$\Delta U=n{C}_v\Delta T$

Since the gas is diatomic.

$\therefore C_v=\frac{5R}{2}$

$\therefore \Delta U=2\times \frac{5R}{2}\times \frac{3}{2R}=7.5L-atm$

Hence the change in interal will be $7.5L-atm$.