A) \[\frac{({{T}_{2}}-{{T}_{1}})\,\,\Delta \,T+{{(\Delta \,T)}^{2}}}{{{T}_{2}}({{T}_{2}}+\Delta \,T)}\]
B) \[\frac{({{T}_{2}}-{{T}_{1}})\,\,\Delta \,T+{{(\Delta \,T)}^{2}}}{{{T}_{1}}({{T}_{1}}+\Delta \,T)}\]
C) \[\frac{({{T}_{1}}-{{T}_{2}})\,\,\Delta \,T+{{(\Delta \,T)}^{2}}}{{{T}_{1}}({{T}_{1}}+\Delta \,T)}\]
D) \[\frac{({{T}_{1}}-{{T}_{2}})\,\,\Delta \,T+{{(\Delta T)}^{2}}}{{{T}_{1}}({{T}_{1}}+\Delta T)}\]
Correct Answer: C
Solution :
\[{{\eta }_{Carnot}}=1-\frac{{{T}_{2}}}{{{T}_{1}}}\] \[{{\eta }_{1}}=1-\frac{{{T}_{2}}-\Delta T}{{{T}_{1}}}\] \[{{\eta }_{2}}=1-\frac{{{T}_{2}}}{{{T}_{1}}+\Delta T}\] \[{{\eta }_{1}}-{{\eta }_{2}}=\frac{{{T}_{2}}}{{{T}_{1}}+\Delta T}-\frac{{{T}_{2}}+\Delta T}{{{T}_{1}}}\] \[=\,\,\frac{{{T}_{1}}{{T}_{2}}-({{T}_{1}}{{T}_{2}}+{{T}_{2}}.\Delta T-{{T}_{1}}.\Delta T-{{\left( \Delta T \right)}^{2}})}{{{T}_{1}}({{T}_{1}}+\Delta T)}\] \[=\,\,\frac{({{T}_{1}}-{{T}_{2}})\,\Delta T+{{(\Delta T)}^{2}}}{{{T}_{1}}({{T}_{1}}+\Delta T)}\]You need to login to perform this action.
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