A) \[\text{(A) 189 K}\text{(B) -2}\text{.7 kj}\]
B) \[\text{(A) 195 K}\text{(B) 2}\text{.7 kj}\]
C) \[\text{(A) 189 K}\text{(B) 2}\text{.7 kj}\]
D) \[\text{(A) 195 K}\text{(B) -2}\text{.7 kj}\]
Correct Answer: A
Solution :
| [a] \[n=2,\,\,{{T}_{1}}=27{}^\circ C=300K,{{V}_{i}}=V,\,\,{{V}_{f}}=2V\] |
| In adiabatic condition |
| \[{{T}_{1}}{{V}_{1}}^{\gamma -1}={{T}_{2}}{{V}_{2}}^{\gamma -1}\] |
| \[300\times {{V}^{(5/3-1)}}={{T}_{2}}{{(2V)}^{5/3-1}}\] |
| \[\Rightarrow {{T}_{2}}\approx 189\] |
| \[\therefore \Delta U=n{{C}_{V}}\Delta T\] |
| As temp decreases so \[\Delta U\] is ve |
| \[\Delta U=2\times \left( \frac{R}{\gamma -1} \right)\Delta T=-2.7kJ\] |
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