question_answer

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 kJ   

C)         20 J                       

D)  -12 kJ

Correct Answer: B

Solution :

For a diatomic gas,                 \[{{C}_{V}}=\frac{5}{2}R\] The change in internal energy of gas in the transition from A to B is \[\Delta U=n{{C}_{v}}dT\]       \[=n\left( \frac{5R}{2} \right)({{T}_{B}}-{{T}_{A}})\] \[=nR\frac{5}{2}\left( \frac{{{p}_{B}}{{V}_{B}}}{nR}\frac{{{p}_{A}}{{V}_{A}}}{nR} \right)\] \[=\frac{5}{2}(2\times {{10}^{3}}\times 6-5\times {{10}^{3}}\times 4)\] \[=\frac{5}{2}\times (-8\times {{10}^{3}})\] \[=-\frac{4\times {{10}^{4}}}{2}=-20KJ\]