Question

A bicycle tyre is filled with air having pressure of 270 kPa at \(27\degree  C\). The approximate pressure of the air in the tyre when the temperature increases to \(36\degree C\) is:

• A. 270 kPa
• B. 278 kPa
• C. 360 kPa
• D. 262 kPa

Hint:

For pressure-temperature problems:

• Use the relation \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \) for constant volume processes.
• Ensure temperature is in Kelvin to avoid errors.

Answer 1

The Correct Option is B

To determine the pressure of the air in the bicycle tyre when the temperature increases, we can utilize the ideal gas law relation for constant volume processes, expressed as:

\[\frac{P_1}{T_1} = \frac{P_2}{T_2}\]

Where:

• P_1 is the initial pressure.
• T_1 is the initial temperature in Kelvin.
• P_2 is the final pressure.
• T_2 is the final temperature in Kelvin.

Let's solve for P_2:

\[P_2 = P_1 \times \frac{T_2}{T_1}\]

Step-by-step Calculation:

1. Convert the given temperatures from Celsius to Kelvin by adding 273:

• Initial temperature, T_1 = 27 + 273 = 300 \, K
• Final temperature, T_2 = 36 + 273 = 309 \, K

2. Substitute the given values into the formula:

\[P_2 = 270 \, \text{kPa} \times \frac{309}{300}\]

3. Calculate P_2:

• P_2 = 270 \times 1.03 = 278.1 \, \text{kPa}

Therefore, the approximate pressure of the air in the tyre when the temperature increases to 36\degree C is around 278 kPa.

This matches with the given correct answer: 278 kPa.