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A perfectly conducting vessel of volume ...

A perfectly conducting vessel of volume ` V = 0.4m^3` contains an ideal gas at constant temperature `T = 273 K`. A portion of the gas is let out and the pressure of the falls by `Delta p = 0.24 atm`. (Density of the gas at (STP) is `rho = 1.2 kg//m^3`). Find the mass of the gas which escapes from the vessel.

Text Solution

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The correct Answer is:
A, B
`p_1 V = n_1 R T`
`p_2 V = n_2 R T` `(T = 273 K)`
`:. (p_1 -p_2) V = (n_1 - n_2)R T = ((m_1 - m_2)/(M)) R T`
`(Delta p)V = (Delta m)/(M) R T`…(i)
In the initial condition (atv STP)
`(R T)/(M) = (p_0)/(rho)`….(ii)
`(T = 273 K)`
From Eqs. (i) and (ii), we get
`Delta m (rho V Deltap)/(p_0) = (1.2 xx 0.4 xx 0.24)/(1.0)`
= `0.1152 kg = 115.2 g`.
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