On a particular hot day, the temperature is 40°C and the partial pressure of water vapor in the air is 38.8 mmHg. What is the relative humidity?

1. Analyze the Question

We are asked to calculate the relative humidity of the air given the current temperature (40°C) and the actual partial pressure of water vapor (38.8 mmHg). To solve this, we need the Saturated Vapor Pressure (SVP) of water at 40°C.

2. Explain the Concept

Relative humidity is defined as the ratio of the actual partial pressure of water vapor in the air to the saturated vapor pressure of water at that same temperature, expressed as a percentage.

Formula:

Note: In physics problems of this nature, if the Saturated Vapor Pressure is not explicitly provided in the question text, it is usually retrieved from standard steam tables or provided in the exam's data sheet. At 40°C, the standard Saturated Vapor Pressure of water is approximately 55.3 mmHg.

3. Show the Solution

• Actual Vapor Pressure: 38.8 mmHg
• Saturated Vapor Pressure (at 40°C): 55.3 mmHg

Using the formula:

4. Identify the Answer

Comparing our result to the given options, the calculated value matches option A.

5. Exam Tip

When dealing with humidity questions in JAMB, always remember that the denominator (Saturated Vapor Pressure) must correspond to the temperature given in the question. If you ever forget the SVP values, look closely at the "Constants" or "Data" section usually provided at the beginning of the Physics exam booklet—they often hide the necessary values there!