Question

Assertion: The air pressure in a car tyre increases during driving.
Reason: Temperature of air in the tyre increases due to friction of tyre with road. Increase in temperature results in an increase in pressure according to Charles’s law.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.

Answer 1

Hint:Recall what causes the increase in tyre temperature while driving. Gay-Lussac’s law relates the temperature of the air with pressure.

Complete answer:
We know that while driving, the temperature of the air inside the tyre increases due to friction between the tyre and the road. The temperature of the air inside the tyre increases but the volume of the air remains constant as the tyre does not undergo expansion. We know that according to Gay-Lussac’s law, at constant volume, the pressure is proportional to the temperature.
\[P \propto T\] at constant \[V\]
Here, P is the pressure, T is the temperature and V is the volume.
Therefore, we can see, as the temperature of air inside the tyre increases, the air pressure increases.

Thus, the reason is the correct explanation of assertion.So, the correct answer is option (A).

Additional information:
Gay-Lussac’s law, Charles’s law, and Boyle’s law are derived from the ideal gas equation, \[PV = nRT\], where, n is number of moles of gas, R is gas constant and T is the temperature. The product \[PV\]is constant for all ideal gases. The temperature in Gay-Lussac’s law should be in Kelvin.

Note:Gay-Lussac’s law is applicable only when the volume of the gas remains constant. If the tyre of a car expands due to increase in temperature, the air pressure will not remain constant according to the gas law. Another way to answer this question is to measure the kinetic energy of the gas inside the tyre. Due to increase in temperature, the molecules of air collide with walls of tyre more rapidly which exerts greater pressure on the tyre.