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JEE Main

Exam: JEE Main
Subject: Physics
Chapter: Kinetic Theory of Gases

JEE Main · Physics · Kinetic Theory of Gases

The temperature of an open room of volume 30m^ 3 increases from 17...

The temperature of an open room of volume

30m^{3}

increases from

17 ° C

to

27 ° C

due to the sunshine. The atmospheric pressure in the room remains

1 \times {10}^{5}Pa

. If

{n}_{i}

and

{n}_{f}

are the number of molecules in the room before and after heating, then

{n}_{f} - {n}_{i}

will be:

Options

A $- 2.5 \times {10}^{25}$
B $- 1.61 \times {10}^{23}$
C $1.38 \times {10}^{23}$
D $2.5 \times {10}^{25}$

Correct answer

A. $- 2.5 \times {10}^{25}$

Step-by-step solution

${T}_{i} = 273 + 17 = 290K$

${T}_{f} = 273 + 27 = 300K$

From ideal gas equation, $PV = nRT ⇒ n = \dfrac{PV}{RT}$

${n}_{f} - {n}_{i} = \dfrac{PV}{R}\left[\dfrac{1}{Tf} - \dfrac{1}{Ti}\right]= - 2.5 \times {10}^{25}$

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