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.                                                                                        [NEET  2015]

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

\[\Delta U=n{{C}_{v}}dT\]

\[=n\left( \frac{5R}{2} \right)({{T}_{B}}-{{T}_{A}})\]

\[=nR\frac{5}{2}\left( \frac{{{p}_{B}}{{V}_{B}}}{nR}\frac{{{p}_{A}}{{V}_{A}}}{nR} \right)\]

\[=\frac{5}{2}(2\times {{10}^{3}}\times 6-5\times {{10}^{3}}\times 4)\]

\[=\frac{5}{2}\times (-8\times {{10}^{3}})\]

\[=-\frac{4\times {{10}^{4}}}{2}=-20KJ\]