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 |
\[\Delta U=n{{C}_{v}}dT\] |
\[=n\left( \frac{5R}{2} \right)({{T}_{B}}-{{T}_{A}})\] |
\[=nR\frac{5}{2}\left( \frac{{{p}_{B}}{{V}_{B}}}{nR}\frac{{{p}_{A}}{{V}_{A}}}{nR} \right)\] |
\[=\frac{5}{2}(2\times {{10}^{3}}\times 6-5\times {{10}^{3}}\times 4)\] |
\[=\frac{5}{2}\times (-8\times {{10}^{3}})\] |
\[=-\frac{4\times {{10}^{4}}}{2}=-20KJ\] |
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