Carnot engine operating between temperatures $T_1$ and $T_2$ has efficiency $0.2$. When $T_2$ is lowered by $45$ K, its efficiency becomes $0.5$. Temperatures $T_1$ and $T_2$ are respectively

Question

A Carnot engine operates between temperatures of $ 600 \, \text{K} $ and $ 300 \, \text{K} $. If it absorbs $ 900 \, \text{J} $ of heat from the source, how much work does it perform?

Answer 1

Step 1: Use the change in efficiency:
The efficiency rises by $0.3$ when $T_2$ falls by 45 K: $\Delta\eta=\dfrac{\Delta T_2}{T_1}$, so $\dfrac{45}{T_1}=0.3$ and $T_1=150$ K.

Step 2: Find T2:
$\eta=0.2$ gives $T_2=T_1(1-0.2)=120$ K.

Step 3: Pick:
$T_1=150$ K, $T_2=120$ K. Option A.

Final Answer:
Lowering T2 by 45 K raises efficiency by 0.3, so T1 = 150 K and T2 = 120 K. \[ \boxed{\text{(A) }150\ \text{K},\ 120\ \text{K}} \]

Carnot engine operating between temperatures \(T_1\) and \(T_2\) has efficiency \(0.2\). When \(T_2\) is lowered by \(45\) K, its efficiency becomes \(0.5\). Temperatures \(T_1\) and \(T_2\) are respectively

Show Hint

The Correct Option is A

Solution and Explanation

Top Questions on carnot cycle

Questions Asked in MHT CET exam