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)

7.5

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6.5

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Solution

The correct option is A 7.5
work done is given as:
$W = P △ V = n R △ T \Rightarrow △ T = \frac{P △ V}{n R}$
Given that: -
$n = 2$ moles
$P = 1$ atm
$V_{i} = 2 L V_{f} = 5 L$
$△ V = V_{f} - V_{i} = 5 - 2 = 3 L ∴ △ T = \frac{1 \times 3}{2 R} = \frac{3}{2 R}$
Now, as we know that internal energy is given as:
$△ U = n C_{v} △ T$
Since the gas is diatomic
$∴ C_{v} = \frac{5 R}{2} ∴ △ U = 2 \times \frac{5 R}{2} \times \frac{3}{2 R} = 7.5 L a t m$

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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)

The correct option is A 7.5work done is given as: W=P△V=nR△T⇒△T=P△VnR Given that: - n=2 moles P=1 atm Vi=2LVf=5L △V=Vf−Vi=5−2=3L∴△T=1×32R=32R Now, as we know that internal energy is given as: △U=nCv△T Since the gas is diatomic ∴Cv=5R2∴△U=2×5R2×32R=7.5L atm