A) \[20%\] and\[-\,43{}^\circ C\]
B) \[40%\]and\[-\,33{}^\circ C\]
C) \[50%\] and\[-\,20{}^\circ C\]
D) \[70%\]and\[-\,10{}^\circ C\]
Correct Answer: B
Solution :
[b] Given: \[{{Q}_{1}}=1000\,J\] \[{{Q}_{2}}=600\,J\] \[{{T}_{1}}=127{}^\circ C=400\,K\] \[{{T}_{2}}=?\] \[\eta =?\] Efficiency of carnot engine, \[\eta =\frac{W}{{{Q}_{1}}}\times 100%\] or, \[\eta =\frac{{{Q}_{2}}-{{Q}_{1}}}{{{Q}_{1}}}\times 100%\] or, \[\eta =\frac{1000-600}{1000}\times 100%\] \[\eta =40%\] Now, for carnot cycle\[\frac{{{Q}_{2}}}{{{Q}_{1}}}=\frac{{{T}_{2}}}{{{T}_{1}}}\] \[\frac{600}{1000}=\frac{{{T}_{2}}}{400}\] \[{{T}_{2}}=\frac{600\times 400}{1000}\] \[=240\,K\] \[=240-273\] \[\therefore \] \[{{T}_{2}}=-33{}^\circ C\]
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