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Physics Question 99 – AP-EAMCET 2025

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The efficiency of a Carnot engine operating between the temperatures 1000 K and 300 K is

The efficiency of a Carnot engine depends only on the temperatures of the hot and cold reservoirs, not on the working substance.

Step 1: Identify Given Temperatures✦ Active

The problem provides the temperatures of the hot and cold reservoirs for a Carnot engine. It is crucial to identify which temperature corresponds to the hot reservoir (Th) and which to the cold reservoir (Tc). The higher temperature is always the hot reservoir, and the lower temperature is the cold reservoir.

Th=1000 K Tc=300 K
💡 Teacher's Secret Hint

Always ensure temperatures are in Kelvin for Carnot efficiency calculations. If given in Celsius, convert them first by adding 273.15.

Step 2: Recall Carnot Efficiency Formula○ Expand

The efficiency of a Carnot engine is determined by the absolute temperatures of its hot and cold reservoirs. The formula for Carnot efficiency (η) is:

η=1−TcTh
💡 Teacher's Secret Hint

The efficiency is always less than 1 (or 100%), as it's impossible to convert all heat into work. A higher temperature difference between Th and Tc leads to higher efficiency.

Step 3: Calculate Efficiency○ Expand

Substitute the identified values of Th and Tc into the efficiency formula and perform the calculation.

η=1−300 K1000 K η=1−0.3 η=0.7
💡 Teacher's Secret Hint

Pay attention to units. Since both temperatures are in Kelvin, their ratio is dimensionless, resulting in a dimensionless efficiency value.

Step 4: Convert to Percentage○ Expand

The calculated efficiency is in decimal form. To express it as a percentage, multiply by 100%.

η=0.7×100% η=70%
💡 Teacher's Secret Hint

Most problems ask for efficiency in percentage, so this final conversion is often necessary. Double-check the question's required format for the answer.

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