If the energy input to a Carnot engine is thrice the work it performs then, the fraction of energy rejected to the sink is

Options

A. `1/3`
B. `1/4`
C. `2/5`
D. `2/3`

Explanation

To solve the problem, we need to find the fraction of energy rejected to the sink by a Carnot engine when the energy input is thrice the work it performs. Let's break this down step by step.

### Step-by-Step Solution:

1. **Define Variables:**
- Let \( Q_1 \) be the heat input to the engine.
- Let \( W \) be the work done by the engine.
- Let \( Q_2 \) be the heat rejected to the sink.

2. **Given Relationship:**
- According to the problem, the energy input \( Q_1 \) is three times the work done \( W \):
\[ Q_1 = 3W \]

3. **Apply the First Law of Thermodynamics:**
- The first law states that the energy input to the system is equal to the work done plus the energy rejected:
\[ Q_1 = W + Q_2 \]

4. **Substitute \( Q_1 \) in the Equation:**
- Replace \( Q_1 \) in the first law equation with \( 3W \):
\[ 3W = W + Q_2 \]

5. **Rearranging the Equation:**
- Now, isolate \( Q_2 \):
\[ Q_2 = 3W - W = 2W \]

6. **Find the Fraction of Energy Rejected:**
- The fraction of energy rejected to the sink is given by the ratio of \( Q_2 \) to \( Q_1 \):
\[ \text{Fraction rejected} = \frac{Q_2}{Q_1} = \frac{2W}{3W} \]

7. **Simplify the Fraction:**
- Simplifying the fraction gives:
\[ \text{Fraction rejected} = \frac{2}{3} \]

### Final Answer:
The fraction of energy rejected to the sink is \( \frac{2}{3} \).