Two rigid vessels A and B , each having a volume of 200 cm^3 , contain an ideal gas ( C_V = 12.5 J K^ -1 mol^ -1 ). These vessels are connected to a manometer tube containing mercury, as shown in the figure. The

Correct answer: D. 0.008 Given: Volume of each vessel, V = 200 cm^3 = 200 × 10^ -6 m^3 Temperature, T = 300 K Pressure, P = 75 cm of Hg = 0.75 m of Hg Gas constant, R = 8.3 J K^ -1 mol^ -1 First, we convert the pressure into SI units (Pascals): P = g h Using density of mercury = 13600 kg m^ -3 and g = 9.8 m s^ -2 : P = 13600 × 9.8 × 0.75 = 99960 Pa Using the ideal gas equation, PV = nRT , we can find the number of moles n in each vessel: n = (PV)/(RT) Substituting the values: n = 99960 × 200 × 10^ -6 8.3 × 300 n = (19.992)/(2490) 0.008 mol The number of moles of the gas in each vessel is 0.008 .

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

Two rigid vessels A and B , each having a volume of 200 cm^3 ,...

Two rigid vessels

A

and

B

, each having a volume of

200 \text{ cm}^3

, contain an ideal gas (

C_V = 12.5 \text{ J K}^{-1} \text{ mol}^{-1}

). These vessels are connected to a manometer tube containing mercury, as shown in the figure. The temperature is

300 \text{ K}

and the pressure in both vessels is

75 \text{ cm}

of mercury. Determine the number of moles of the gas in each vessel. Use the gas constant

R = 8.3 \text{ J K}^{-1} \text{ mol}^{-1}

Two rigid vessels A and B , each having a volume of 200 cm^3 , contain an ideal gas ( C_V = 12.5 J K^ -1 mol^ -1 ).

Options

A $0.016$
B $0.024$
C $0.004$
D $0.008$

Correct answer

D. $0.008$

Step-by-step solution

Given:
Volume of each vessel,

V = 200 \text{ cm}^3 = 200 \times 10^{-6} \text{ m}^3

Temperature,

T = 300 \text{ K}

Pressure,

P = 75 \text{ cm of Hg} = 0.75 \text{ m of Hg}

Gas constant,

R = 8.3 \text{ J K}^{-1} \text{ mol}^{-1}

First, we convert the pressure into SI units (Pascals):

P = \rho g h

Using density of mercury

\rho = 13600 \text{ kg m}^{-3}

and

g = 9.8 \text{ m s}^{-2}

P = 13600 \times 9.8 \times 0.75 = 99960 \text{ Pa}

Using the ideal gas equation,

PV = nRT

, we can find the number of moles

n

in each vessel:

n = \dfrac{PV}{RT}

Substituting the values:

n = \dfrac{99960 \times 200 \times 10^{-6}}{8.3 \times 300}

n = \dfrac{19.992}{2490} \approx 0.008 \text{ mol}

The number of moles of the gas in each vessel is

0.008

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