A) 0.28
B) 2.8
C) 28
D) 0.028
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 the total heat supplied to the engine which is converted into work that is \[\eta =\frac{W}{{{Q}_{1}}}=\frac{{{Q}_{1}}-{{Q}_{2}}}{{{Q}_{1}}}=1-\frac{{{Q}_{2}}}{{{Q}_{1}}}=1-\frac{{{T}_{2}}}{{{T}_{1}}}\] Given, \[{{T}_{2}}={{27}^{o}}C=273+27=300K,\] \[{{T}_{1}}=677{}^\circ C=677+273=950\text{ }K\] \[\therefore \] \[\eta =1-\frac{{{T}_{2}}}{{{T}_{1}}}=1-\frac{300}{950}=\frac{13}{19}\] \[\therefore \] \[W=\eta {{Q}_{1}}=100\times {{10}^{3}}\times \frac{13}{19}cal\] Also \[4.2\text{ }J=1\text{ }cal\] \[\therefore \] \[W=100\times {{10}^{3}}\times \frac{13}{19}\times 4.2\] \[W=2.87\times {{10}^{5}}\] \[W=0.28\times {{10}^{6}}J\]
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