One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown in the figure. The change in internal energy of the gas during the transition is [2015]

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Solution

Q.
One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown in the figure. The change in internal energy of the gas during the transition is [2015]

1 20 J

2 - 12 kJ

3 20 kJ

4 - 20 kJ

Ans.
(4)

We know, $Δ U = n C_{V} Δ T$

$= n (\frac{5 R}{2}) (T_{B} - T_{A})$ [For diatomic gas, $C_{V} = \frac{5 R}{2}$ ]

$= \frac{5 n R}{2} (\frac{P_{B} V_{B}}{n R} - \frac{P_{A} V_{A}}{n R})$ $[∵ P V = n R T]$

$= \frac{5}{2} (P_{B} V_{B} - P_{A} V_{A}) = \frac{5}{2} (2 \times 10^{3} \times 6 - 5 \times 10^{3} \times 4)$

$= \frac{5}{2} (- 8 \times 10^{3}) = - 20$ $kJ$

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