On a particular hot day the temperature is 40 C... - JAMB Physics 2023 Question

To calculate relative humidity, you can use the formula:

\[ \text{Relative Humidity (\%)} = \left( \frac{\text{Partial Pressure of Water Vapor}}{\text{Saturation Vapor Pressure at the Given Temperature}} \right) \times 100 \]

The saturation vapour pressure is the maximum pressure that water vapor can exert at a given temperature. It depends on the temperature and is a function of the water vapor pressure at 100% humidity.

The saturation vapour pressure at 40°C can be obtained from tables or calculations. For this example, let's assume it's \(50 \, \text{mmHg}\).

Now, substitute the given values into the formula:

\[ \text{Relative Humidity (\%)} = \left( \frac{38.8}{50} \right) \times 100 \]

\[ \text{Relative Humidity (\%)} \approx 77.6 \]

So, the closest option is: 70

Please note that the saturation vapour pressure at 40°C may vary slightly depending on the source used, and it's advisable to use accurate data for precise calculations.