Question

An ideal heat engine working between temperature $T$ and $T^{\prime }$ has efficiency $\eta$. If both the temperatures are raised by $100K$ each, the new efficiency of the heat engine will be

• A. Equal to $\eta$
• B. Greater to $\eta$
• C. Less than $\eta$
• D. Greater or less than $\eta$ depending upon the nature of the working substances

Answer 1

Answer: (C)

Less than $\eta$

Initial efficiency of the engine $\eta =\frac{T^{\prime }-T}{T^{\prime }}$
If both the temperatures are increased by $100K$,
Thus new efficiency
${\eta }^{\prime }=\frac{(T^{\prime }+100)-(T+100)}{(T^{\prime }+100)}=\frac{T^{\prime }-T}{T^{\prime }+100}$
That is ${\eta }^{\prime }<\eta$.