Kinetic Theory - Result Question 25

25. 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:

(a) $-20 kJ$

(b) $20 J$

(c) $-12 kJ$

(d) $20 kJ$

[2015]

Show Answer

Answer:

Correct Answer: 25. (a)

Solution:

  1. (a) Change in internal energy from $A \to B$

$\Delta U=\frac{f}{2} nR \Delta T=\frac{f}{2} nR(T_f-T_i)$

$=\frac{5}{2}{P_f V_f-P_i V_i}$

$=\frac{5}{2}{2 \times 10^{3} \times 6-5 \times 10^{3} \times 4}$

$=\frac{5}{2}{12-20} \times 10^{3} J=5 \times(-4) \times 10^{3} J$

$\Delta U=-20 KJ$

(As gas is diatomic $\therefore f=5$ )