A) 372 K, 310 K
B) 181 K, 150 K
C) 472 K, 410 K
D) none of the above
Correct Answer: A
Solution :
A heat engine is a device which converts heat energy into mechanical energy efficiency of heat engine is the fraction of total heat supplied to the engine which is converted into work. \[\eta =\frac{H}{Q}=1-\frac{{{Q}_{2}}}{{{Q}_{1}}}=1-\frac{{{T}_{2}}}{{{T}_{1}}}\] where \[{{T}_{1}}\] is temperature of source and \[{{T}_{2}}\] is temperature of sink. Given, \[{{\eta }_{1}}=\frac{1}{6},\,{{\eta }_{2}}=\frac{1}{3}\] \[\therefore \] \[\frac{1}{6}=\frac{{{T}_{1}}-{{T}_{2}}}{{{T}_{1}}}\] ?. (i) and \[\frac{1}{3}=\frac{{{T}_{1}}-({{T}_{2}}-62)}{{{T}_{1}}}\] ... (ii) Solving Eqs. (i) and (ii), we get \[{{T}_{1}}=372\,K\] and \[{{T}_{2}}=310\,K\] Note: Temperature of source in a heat engine is always greater than temperature of sink.
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