question_answer 27)

                  Consider a Carnot's cycle operating between \[{{T}_{1}}\,=500\,K\] and \[{{T}_{2}}\,=300\,K\] producing 1 kJ of mechanical work per cycle. Find die heat transferred to the engine by the reservoirs.                

Answer:

                  \[\eta =\,1-\frac{{{T}_{2}}}{{{T}_{1}}}=1-\,\frac{3}{5}=\frac{2}{5}\]                           \[\eta \,=\,\frac{W}{{{Q}_{1}}}\,\therefore \,{{Q}_{1}}\,=\frac{W}{\eta }=\,\frac{1000\,J}{2/5}\,=2500\,J\]                 \[\therefore \] \[{{Q}_{2}}=\,{{Q}_{1}}-W=2500\,\,-1000\,\,=1500\,J\]