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

JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Heat & Thermodynamics

A bicycle tyre is filled with air having pressure of 270 kPa at

2 7^{\circ} C

. The approximate pressure of the air in the tyre when the temperature increases to

3 6^{\circ} C

(A)270 kPa
(B)262 KPa
(C)278 kPa✓ Correct
(D)360 kPa

Answer: (C)

Solution

At fixed volume the pressure of a gas is proportional to its absolute temperature,

\frac{P _{1}}{T _{1}} = \frac{P _{2}}{T _{2}}

. With

T_{1} = 300

K and

T_{2} = 309

P_{2} = 270 \times \frac{309}{300}

. The pressure rises to about

278

kPa.

JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Single correct option

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