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

Correct answer: C. 278 kPa From the ideal gas equation PV=nRT Here, volume is constant P_1 T_1 = P_2 T_2 Here, T_1=27+273=300 K P_1=270 kPa T_2=36+273=309 K P_2=(P_1)/(T_1) × T_2=(270 ×(309))/(300)=278 kPa

BITSAT 2023Paper 1

Exam: BITSAT
Year: 2023
Paper: Paper 1
Subject: Physics
Chapter: Kinetic Theory of Gases

BITSAT 2023 · Paper 1 · Physics · Kinetic Theory of Gases

A bicycle tyre is filled with air having pressure of 270 kPa at 27^...

A bicycle tyre is filled with air having pressure of

270 \mathrm{kPa}

27^{{}^{\circ}} \mathrm{C}

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

36^{{}^{\circ}} \mathrm{C}

Options

A $270 \mathrm{kPa}$
B $262 \mathrm{KPa}$
C $278 \mathrm{kPa}$
D $360 \mathrm{kPa}$

Correct answer

C. $278 \mathrm{kPa}$

Step-by-step solution

From the ideal gas equation

\mathrm{PV}=\mathrm{nRT}

Here, volume is constant

\therefore \frac{\mathrm{P}_1}{\mathrm{ T}_1}=\frac{\mathrm{P}_2}{\mathrm{ T}_2}

Here,

T_1=27+273=300 \mathrm{ K}

P_1=270 \mathrm{kPa}

\mathrm{T}_2=36+273=309 \mathrm{ K}

\Rightarrow P_2=\frac{P_1}{T_1} \times T_2=\frac{270 \times(309)}{300}=278 \mathrm{kPa}

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