If the volume of a given mass of a gas at 0ºc is 29.5cm$^3$. What will be the volume of the gas at 15ºc, given that the pressure remains constant.

1. Analyze the question

We are given the initial volume ($V_1$) and initial temperature ($T_1$) of a gas. We need to find the new volume ($V_2$) at a new temperature ($T_2$), while the pressure remains constant. This is a classic application of Charles's Law.

2. Explain the concept

Charles's Law states that for a fixed mass of gas at constant pressure, the volume is directly proportional to its absolute temperature (measured in Kelvin).

The formula is:

Important Note: In gas law calculations, temperatures must always be converted from Celsius (°C) to Kelvin (K) by adding 273.15 (or simply 273 for most JAMB calculations).

3. Show the solution

Step 1: List the given values

• $V_1 = 29.5 \text{ cm}^3$
• $T_1 = 0^\circ\text{C} = 0 + 273 = 273 \text{ K}$
• $T_2 = 15^\circ\text{C} = 15 + 273 = 288 \text{ K}$
• $V_2 = ?$

Step 2: Rearrange the formula to solve for $V_2$

Step 3: Substitute the values into the equation

Step 4: Calculate the result

Rounding to one decimal place, we get 31.1 cm³.

4. Identify the answer

Comparing our result to the given options, the correct choice is D.

5. Tip

Always remember the "Kelvin Rule": If you forget to convert Celsius to Kelvin in a gas law problem, you will almost certainly get the wrong answer. A quick way to check your work is to see if the volume changed in the same direction as the temperature—since the temperature increased, the volume must also increase.