A) \[A({{T}_{2}}-{{T}_{1}})+B(T_{2}^{2}-T_{1}^{2})\]
B) \[\frac{A({{T}_{2}}-{{T}_{1}})}{{{V}_{2}}-{{V}_{1}}}-\frac{B(T_{2}^{2}-T_{1}^{2})}{{{V}_{2}}-{{V}_{1}}}\]
C) \[A({{T}_{2}}-{{T}_{1}})-\frac{B}{2}(T_{2}^{2}-T_{1}^{2})\]
D) \[\frac{A({{T}_{2}}-T_{1}^{2})}{{{V}_{2}}-{{V}_{1}}}\]
Correct Answer: C
Solution :
Given, \[P=\frac{AT-B{{T}^{2}}}{V}\] \[\Rightarrow \]\[PV=AT-B{{T}^{2}}\Rightarrow P\Delta V=A\Delta T-BT\Delta T\]On integrating, we get \[\text{Work}\,\text{=}\,\int_{{}}^{{}}{PdV}=A\int_{{{T}_{1}}}^{{{T}_{2}}}{dT-}B\int_{{{T}_{1}}}^{{{T}_{2}}}{TdT}\] \[=A({{T}_{2}}-{{T}_{1}})-\frac{B}{2}[{{({{T}_{2}})}^{2}}-{{({{T}_{1}})}^{2}}]\]You need to login to perform this action.
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