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:
Show 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.
- 270 kPa
- 278 kPa
- 360 kPa
- 262 kPa
The Correct Option is B
Solution and Explanation
- Pressure-Temperature Relation: Using Gay-Lussac’s law (volume is constant): \[ \frac{P_1}{T_1} = \frac{P_2}{T_2}. \]
- Substitute Values: \( P_1 = 270 \, \text{kPa}, \, T_1 = 300 \, \text{K}, \, T_2 = 309 \, \text{K} \): \[ P_2 = P_1 \times \frac{T_2}{T_1} = 270 \times \frac{309}{300}. \]
- Calculate \( P_2 \): \[ P_2 \approx 278 \, \text{kPa}. \]
Final Answer: \( \boxed{278 \, \text{kPa}} \)
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