In a motor the electrical power input is 500 W and the mechanical power output is 0.54 horse power. Heat developed in the motor in 1 h is (assuming that all the electric energy which is not converted to mechanical energy is converted to heat) is

Options

A. `4.18xx10^4cal`
B. `3.6xx10^5cal`
C. `8.6xx10^4cal`
D. `1.28xx10^5cal`

Explanation

To solve the problem step by step, we need to calculate the heat developed in the motor in one hour based on the given electrical power input and mechanical power output.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Electrical power input (P_input) = 500 W
- Mechanical power output (P_output) = 0.54 horsepower

2. **Convert Horsepower to Watts:**
- 1 horsepower = 746 W
- Therefore, P_output in watts = 0.54 * 746 = 402.84 W

3. **Calculate the Efficiency of the Motor:**
- Efficiency (η) = (P_output / P_input)
- η = (402.84 W / 500 W) = 0.80568 (approximately 0.81 or 81%)

4. **Determine the Power Converted to Heat:**
- The power that is not converted to mechanical energy is converted to heat.
- Heat power (P_heat) = P_input - P_output
- P_heat = 500 W - 402.84 W = 97.16 W

5. **Calculate Heat Developed in One Hour:**
- Heat energy in one hour = P_heat * time
- Time = 1 hour = 3600 seconds
- Heat energy = 97.16 W * 3600 s = 349,776 J

6. **Convert Joules to Calories:**
- 1 calorie = 4.18 J
- Heat in calories = Heat in joules / 4.18
- Heat in calories = 349,776 J / 4.18 = 83,600.19 calories (approximately 8.36 x 10^4 calories)

### Final Answer:
The heat developed in the motor in one hour is approximately **8.36 x 10^4 calories**.

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