Source temperature of a carnot engine is 127 celsius if efficiency of carnot engine is 60% then find sink temperature

Answer

To solve the problem of finding the sink temperature of a Carnot engine given the source temperature and efficiency, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Source temperature (T2) = 127 °C
- Efficiency (η) = 60% = 0.60

2. **Convert Source Temperature to Kelvin:**
- The temperature in Kelvin is calculated by adding 273 to the Celsius temperature.
\[ T2 = 127 + 273 = 400 \, K \]

3. **Use the Efficiency Formula for a Carnot Engine:**
- The efficiency of a Carnot engine is given by the formula:
\[ \eta = 1 - \frac{T1}{T2} \]
where T1 is the sink temperature.

4. **Substitute the Known Values into the Efficiency Formula:**
- Rearranging the formula to solve for T1:
\[ 0.60 = 1 - \frac{T1}{400} \]

5. **Rearranging the Equation:**
- Move \(\frac{T1}{400}\) to the left side:
\[ \frac{T1}{400} = 1 - 0.60 \]
\[ \frac{T1}{400} = 0.40 \]

6. **Solve for T1:**
- Multiply both sides by 400:
\[ T1 = 0.40 \times 400 = 160 \, K \]

7. **Convert Sink Temperature to Celsius:**
- To convert Kelvin back to Celsius:
\[ T1 = 160 - 273 = -113 \, °C \]

### Final Answer:
The sink temperature (T1) is **160 K** or **-113 °C**.

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