Match the temperatures of the source and sink ( $T_1$ and $T_2$ respectively) of a Carnot heat engine given…
Match the temperatures of the source and sink ( $T_1$ and $T_2$ respectively) of a Carnot heat engine given in List-I with the corresponding efficiencies given in List-II.
The correct match is Codes
$\begin{array}{llll}
A & B & C & D
\end{array}$
(iii) (iv (ii) (i)
(iv) (iii) (ii) (i)
(iii) (i) (iv) (ii)
(iii) (ii) (iv) (i)
Solution
Key Ideal Efficiency of a Carnot engine is given as,
$
\eta=1-\frac{T_2}{T_1}
$
where, $T_1=$ surface temperature and $T_2=\sin k$ temperature.
Now, the efficiencies are,
(a) When $T_1=500 \mathrm{~K}, T_2=300 \mathrm{~K} \Rightarrow \eta=1-\frac{300}{500}=0.4$
(b) When $T_1=500 \mathrm{~K}, T_2=350 \mathrm{~K} \Rightarrow \eta=1-\frac{350}{500}=0.3$
(c) When $T_1=800 \mathrm{~K}, T_2=400 \mathrm{~K} \Rightarrow \eta=1-\frac{400}{800}=0.5$
(d) When $T_1=450 \mathrm{~K}, T_2=360 \mathrm{~K} \Rightarrow \eta=1-\frac{360}{450}=0.2$
Hence, the correct code is matches to option (d)
