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Properties of Matter question

2023 · 29 Jan · Shift 1 · Q63

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JEE Main
Physics
Properties of Matter
2023 · 29 Jan · Shift 1 · Q63

Properties of Matter question

2023 · 29 Jan · Shift 1 · Q63

JEE MainPhysicsProperties of MatterMCQ+4 / −1

A bicycle tyre is filled with air having pressure of

270 ~\mathrm{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

A
262 kPa
B
360 kPa
C
270 kPa
D
278 kPa

View written solutionFree

Correct answer: D

Use Gay-Lussac’s law for a fixed mass of gas at constant volume:

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

Here,

Initial pressure: $P_1=270\,\text{kPa}$
Initial temperature: $T_1=27^\circ\text{C}=300\,\text{K}$
Final temperature: $T_2=36^\circ\text{C}=309\,\text{K}$

Calculate final pressure:

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

$P_2=270\times \frac{309}{300}$

$P_2=270\times 1.03=278.1\,\text{kPa}$

Approximate value:

$P_2\approx 278\,\text{kPa}$

Evaluate options:

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

Therefore, the correct answer is D.

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