Question

An engine having an efficiency of $0.6$ has an exhaust, which is used to drive another engine with an efficiency of $0.4$. The efficiency of the system of two engines as a whole is

• A. $0.5$
• B. $0.2$
• C. $1.0$
• D. $0.76$

Answer 1

Answer: (D)

$0.76$

For the first engine,

$\eta =1-\frac{T_2}{T_1}=0.6\Rightarrow T_1=2.5T_2$

$T_1$=Hot side temperature

$T_2$=Cold side temperature

For the second engine,

$\eta =1-\frac{T_3}{T_2}=0.4\Rightarrow T_3=0.6T_2$

Combined efficiency

${\eta }_{total}=1-\frac{T_3}{T_1}$

$\eta =1-\frac{{0.6T}_2}{{2.5T}_2}=0.76$

Hence,Option D is correct