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

work done is given as:
$W=P△V=nR△T\Rightarrow △T=\frac{P△V}{nR}$
Given that: -
$n=2$ moles
$P=1$ atm
$V_i=2L{V}_f=5L$
$△V=V_f-V_i=5-2=3L\therefore △T=\frac{1\times 3}{2R}=\frac{3}{2R}$
Now, as we know that internal energy is given as:
$△U=n{C}_v△T$
Since the gas is diatomic
$\therefore C_v=\frac{5R}{2}\therefore △U=2\times \frac{5R}{2}\times \frac{3}{2R}=7.5Latm$