Question

The efficiency of a Carnot engine depends on:

• A. Pressure
• B. Volume
• C. Temperatures of reservoirs
• D. Working substance

Hint:

Carnot efficiency is an upper-bound limit for any heat engine.
Always use absolute temperatures in Kelvin when calculating Carnot efficiency:
$\eta = 1 - \frac{T_{\text{cold}}}{T_{\text{hot}}}$

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks which factor determines the efficiency of a Carnot cycle heat engine.

Step 2: Key Formula or Approach:
The thermal efficiency ($\eta$) of a reversible Carnot engine operating between a hot reservoir at absolute temperature $T_H$ and a cold reservoir at temperature $T_C$ is:
\[ \eta = 1 - \frac{T_C}{T_H} \]

Step 3: Detailed Explanation:

• According to Carnot's theorem, no engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between those same reservoirs.

• The formula shows that the efficiency ($\eta$) is purely a function of the absolute temperatures $T_H$ and $T_C$.

• It is completely independent of the nature of the working fluid (whether it is an ideal gas, steam, or any other substance), the operating pressures, or the volume limits of the cycle.

• To increase the efficiency, one must either increase the source temperature ($T_H$) or decrease the sink temperature ($T_C$).

Step 4: Final Answer:
The efficiency depends on the temperatures of the reservoirs.