Question

One reversible heat engine operates between 1600 K and $T_2$ K, and another reversible heat engine operates between $T_2$ K and 400 K. If both the engines have the same heat input and output, then the temperature $T_2$ must be equal to:

• A. $600$
• B. $800$
• C. $650$
• D. $675$

Answer 1

The correct option is B $800$

$T_1=1600K$

$T_2=T_{2}K$

$T_1^1=T_{2}K$

$T_2^1=400K$

Same input and same output.Then the efficiency is same.

$\eta =\frac{T_1-T_2}{T_1}$

$\therefore \frac{1600-T_2}{1600}=\frac{T_2-400}{T_2}$

$=1600T_2-T_2^2=1600T_2-640000$

$\therefore T_2^2=640000$

$\therefore T_2=800K$