An ideal gas sample ( γ = 1.5 ) is adiabatically compressed from a volume of 150 cm^3 to 50 cm^3 . The initial pressure and initial temperature are 150 kPa and 300 K . Determine the number of moles of the gas in the

Correct answer: C. 0.009 Using the ideal gas equation for the initial state: P_1 V_1 = n R T_1 Substituting the given values P_1 = 150 × 10^3 Pa , V_1 = 150 × 10^ -6 m^3 , T_1 = 300 K , and R = (25)/(3) J/(mol K) : n = 150 × 10^3 × 150 × 10^ -6 (25)/(3) × 300 n = (22.5)/(2500) n = 0.009 moles

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 sample ( γ = 1.5 ) is adiabatically compressed from a...

An ideal gas sample (

\gamma = 1.5

) is adiabatically compressed from a volume of

150 \text{ cm}^3

50 \text{ cm}^3

. The initial pressure and initial temperature are

150 \text{ kPa}

and

300 \text{ K}

. Determine the number of moles of the gas in the sample.

Options

A $0.018$
B $0.0045$
C $0.009$
D $0.045$

Correct answer

C. $0.009$

Step-by-step solution

Using the ideal gas equation for the initial state:

P_1 V_1 = n R T_1

Substituting the given values

P_1 = 150 \times 10^3 \text{ Pa}

V_1 = 150 \times 10^{-6} \text{ m}^3

T_1 = 300 \text{ K}

, and

R = \dfrac{25}{3} \text{ J/(mol K)}

n = \dfrac{150 \times 10^3 \times 150 \times 10^{-6}}{\dfrac{25}{3} \times 300}

n = \dfrac{22.5}{2500}

n = 0.009 \text{ moles}

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