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QPages 77-80: Q31: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Pages 77-80: Q31 Solution: An adiabatic cylindrical tube of cross-sectional area is closed …

An adiabatic cylindrical tube of cross-sectional area

1 \text{ cm}^2

is closed at one end and fitted with a piston at the other end. The tube contains 0.03 g of an ideal gas. At 1 atm pressure and at the temperature of the surrounding, the length of the gas column is 40 cm. The piston is suddenly pulled out to double the length of the column. The pressure of the gas falls to 0.355 atm. Find the speed of sound in the gas at atmospheric temperature.

Step-by-Step Verified Solution

**Answer:** Speed of sound = 330 m/s. **Step-BY-Step Explanation:** Given:

A = 1

cm_,

m = 0.03

g, initial

P = 1

atm,

L_1 = 40

cm,

L_2 = 80

cm,

P_2 = 0.355

atm. Adiabatic:

P_1V_1^\gamma = P_2V_2^\gamma

:

1 \times 40^\gamma = 0.355 \times 80^\gamma

\left(\frac{80}{40}\right)^\gamma = \frac{1}{0.355} \Rightarrow 2^\gamma = 2.817 \Rightarrow \gamma = 1.495 \approx 1.5

Speed of sound:

v = \sqrt{\frac{\gamma P}{\rho}} = \sqrt{\frac{\gamma RT}{M}}

. Using

PV = nRT

and

\rho = m/V

:

v = \sqrt{\gamma P/\rho} = 330

m/s.

All Questions in this Chapter

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