A Carnot engine operates between a hot source and a cold sink, initially having a thermal efficiency — Thermodynamics and Thermochemistry Chemistry Question
Question
A Carnot engine operates between a hot source and a cold sink, initially having a thermal efficiency of 40%. When the temperature of the sink is reduced by 60 C, the efficiency increases to 55%. What are the original absolute temperatures of the source ($T_H$) and sink ($T_C$)?
Answer: A
💡 Solution & Explanation
$\eta_1 = 1 - T_C/T_H = 0.4 \Rightarrow T_C/T_H = 0.6$. After reducing sink, $\eta_2 = 1 - (T_C - 60)/T_H = 0.55 \Rightarrow (T_C - 60)/T_H = 0.45$. Thus, $T_C/T_H - 60/T_H = 0.45 \Rightarrow 0.6 - 60/T_H = 0.45 \Rightarrow 60/T_H = 0.15 \Rightarrow T_H = 400$ K. $T_C = 0.6 \times 400 = 240$ K.
💬Ask on WhatsApp →
Still have doubts about this question?
Send it to our AI chemistry tutor on WhatsApp — gets answered in minutes