Question

The efficiency of a Carnot cycle is determined by:

• A. The difference in temperature between the hot and cold reservoirs
• B. The total work done during the cycle
• C. The amount of heat absorbed in the process
• D. The specific heat capacities of the substances involved

Hint:

Carnot efficiency depends only on the temperatures of the heat source and sink—maximize \( T_H \), minimize \( T_C \) for higher efficiency.

Answer 1

The Correct Option is A

Step 1: The Carnot cycle is an idealized thermodynamic cycle that represents the maximum possible efficiency any heat engine can achieve between two temperature reservoirs. 
Step 2: The efficiency \( \eta \) of a Carnot engine is given by: \[ \eta = 1 - \frac{T_C}{T_H} \] where \( T_H \) is the absolute temperature of the hot reservoir and \( T_C \) is the absolute temperature of the cold reservoir (in Kelvin). 
Step 3: This formula shows that the efficiency depends solely on the temperatures of the reservoirs and not on the working substance, the heat absorbed, or the specific heat capacities. 

Why the other options are incorrect:

• (B) Work output depends on the specific process and does not define Carnot efficiency.
• (C) Heat absorbed affects energy flow but not the ideal efficiency formula.
• (D) Specific heat capacities are irrelevant to the Carnot efficiency expression.