Concept explainers
(a)
To Find: The height of the gas column.
(a)
Explanation of Solution
Given:
Number of moles of gas,
At STP, volume is
Mass of the piston,
Formula Used:
Here, P is the pressure, V is the volume, R is the gas constant, n is the number of moles and T is the temperature.
Calculations:
Pressure inside the cylinder:
Substitute the values:
Conclusion:
Thus, the height of the gas column is 2.1 m.
(b)
To Find:The frequency of vibration of piston.
(b)
Explanation of Solution
Given:
Number of moles of gas,
At STP, volume is
Mass of the piston,
Formula Used:
Frequency of vibration of piston can be obtained by:
Here, m is the mass and kis the stiffness constant.
Calculations
In equilibrium position:
Let the displacement from the equilibrium position be x .
From ideal gas law:
Condition of S.H.M:
Substitute the values and solve:
Conclusion:
Thus, the frequency of vibration of piston is 1.0 Hz.
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Chapter 17 Solutions
Physics for Scientists and Engineers, Vol. 3
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