An ideal gas expands from 100 cm^3 to 200 cm^3 at a constant pressure of 2.0 × 10^5 Pa upon being supplied with 50 J of heat. Determine the number of moles in the gas if its initial temperature is 300 K . (Take R = 8.31

Correct answer: B. 0.008 Using the ideal gas equation for the initial state: P V_1 = n R T_1 Substituting the given values: P = 2.0 × 10^5 Pa V_1 = 100 cm^3 = 100 × 10^ -6 m^3 = 10^ -4 m^3 T_1 = 300 K R = 8.31 J K^ -1 mol^ -1 n = 2.0 × 10^5 × 10^ -4 8.31 × 300 n = (20)/(2493) 0.008 mol

Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Specific Heat Capacities of Gases

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Specific Heat Capacities of Gases

An ideal gas expands from 100 cm^3 to 200 cm^3 at a constant...

An ideal gas expands from

100 \text{ cm}^3

200 \text{ cm}^3

at a constant pressure of

2.0 \times 10^5 \text{ Pa}

upon being supplied with

50 \text{ J}

of heat. Determine the number of moles in the gas if its initial temperature is

300 \text{ K}

. (Take

R = 8.31 \text{ J K}^{-1} \text{ mol}^{-1}

)

Options

A $0.012$
B $0.008$
C $0.004$
D $0.016$

Correct answer

B. $0.008$

Step-by-step solution

Using the ideal gas equation for the initial state:

P V_1 = n R T_1

Substituting the given values:

P = 2.0 \times 10^5 \text{ Pa}

V_1 = 100 \text{ cm}^3 = 100 \times 10^{-6} \text{ m}^3 = 10^{-4} \text{ m}^3

T_1 = 300 \text{ K}

R = 8.31 \text{ J K}^{-1} \text{ mol}^{-1}

n = \dfrac{2.0 \times 10^5 \times 10^{-4}}{8.31 \times 300}

n = \dfrac{20}{2493} \approx 0.008 \text{ mol}

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