A bicycle tyre is filled with air at a pressure of 270 kPa at 27^ C. The approximate pressure of the air in the tyre when the temperature increases to 36^ C is:

Given: Initial pressure is P1 = 270 kPa, initial temperature is T1 = 300 K, and final temperature is T2 = 309 K. Find: The final pressure P2 of the air in the tyre. At constant volume, use Gay-Lussac’s law: P1T1 = P2T2 Substituting the values shown in the solution: P2 = P1 T2T1 = 270 309300 Therefore, P2 278 kPa So the calculated value is 278 kPa. The solution concludes this value, although it also states 'The Correct Option is B', which disagrees with the listed options. Since 278 kPa corresponds to option C, the defensible correct option from the working is C.

A bicycle tyre is filled with air at a pressure of 270 kPa at 27^… — Solution | JEE Physics

MCQEasyJEE 2023Equation of State of Ideal Gas

A bicycle tyre is filled with air at a pressure of $270 \, \text{kPa}$ at $27^\circ \text{C}$ . The approximate pressure of the air in the tyre when the temperature increases to $36^\circ \text{C}$ is:

A
$270 \, \text{kPa}$
B
$262 \, \text{kPa}$
C
$278 \, \text{kPa}$
D
$360 \, \text{kPa}$

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: Initial pressure is $P_1 = 270 \, \text{kPa}$ , initial temperature is $T_1 = 300 \, \text{K}$ , and final temperature is $T_2 = 309 \, \text{K}$ .

Find: The final pressure $P_2$ of the air in the tyre.

At constant volume, use Gay-Lussac’s law:

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

Substituting the values shown in the solution:

P_2 = P_1 \times \frac{T_2}{T_1} = 270 \times \frac{309}{300}

Therefore,

P_2 \approx 278 \, \text{kPa}

So the calculated value is $278 \, \text{kPa}$ . The solution concludes this value, although it also states 'The Correct Option is B', which disagrees with the listed options. Since $278 \, \text{kPa}$ corresponds to option C, the defensible correct option from the working is C.

Common mistakes

Using temperature in degree Celsius directly in $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ is incorrect because gas-law ratios require absolute temperature. Convert to Kelvin first.
Assuming pressure remains unchanged because the tyre volume is nearly constant is wrong. At constant volume, pressure increases with temperature.
Selecting the option label from the page heading without checking the calculation can be misleading here. Verify the numerical result from the working and then match it to the options.

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