Question

An ideal Carnot engine working with source temperature T₁, and sink temperature T₂, has efficiency n. Then the value of the ratio \(\frac{T_1}{T_2}\) is

• A. \(\frac{1}{1-n}\)
• B. \(\frac{1-n}{1}\)
• C. \(\frac{1}{n}\)
• D. n
• E. \(\frac{n}{1-n}\)

Answer 1

The Correct Option is A

The efficiency \( \eta \) of a Carnot engine is given by the formula: \[ \eta = 1 - \frac{T_2}{T_1} \] Rearranging this equation to solve for \( \frac{T_1}{T_2} \), we get: \[ \frac{T_1}{T_2} = \frac{1}{1 - \eta} \]

Thus, the correct answer is (A): \( \frac{1}{1 - \eta} \).

Answer 2

The efficiency of an ideal Carnot engine is given by:  

$$ \eta = 1 - \frac{T_2}{T_1} $$ 
Rearranging to find the ratio \( \frac{T_1}{T_2} \): 
$$ \frac{T_2}{T_1} = 1 - \eta $$ 
Taking reciprocal: $$ \frac{T_1}{T_2} = \frac{1}{1 - \eta} $$ 
Correct answer: \( \frac{1}{1 - n} \)