A carnot engine working between -10 deg C and 25 deg C temperature limit if produce a power of 35 W then what is heat input rate in engine.

Options

A. 190J
B. 290J
C. 298J
D. 250J

Answer

To solve the problem of finding the heat input rate in a Carnot engine operating between two temperature limits, we can follow these steps:

### Given Data:
- Temperature of the cold reservoir (T_c) = -10 °C = 263 K (in Kelvin)
- Temperature of the hot reservoir (T_h) = 25 °C = 298 K (in Kelvin)
- Power output (W) = 35 W

### Step 1: Calculate the Efficiency of the Carnot Engine
The efficiency (η) of a Carnot engine is given by the formula:
\[ \eta = 1 - \frac{T_c}{T_h} \]
Substituting the values:
\[ \eta = 1 - \frac{263}{298} \]
Calculating this gives:
\[ \eta = 1 - 0.882 = 0.118 \]

### Step 2: Relate Power Output to Heat Input
The power output (W) of the engine can also be expressed in terms of the heat input (Q_h) and efficiency (η) as follows:
\[ W = \eta \cdot Q_h \]
Rearranging this to find Q_h gives:
\[ Q_h = \frac{W}{\eta} \]

### Step 3: Substitute the Known Values
Now, substituting the values we have:
\[ Q_h = \frac{35 \text{ W}}{0.118} \]
Calculating this gives:
\[ Q_h \approx 296.61 \text{ W} \]

### Conclusion
The heat input rate in the engine is approximately **296.61 W**.

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