A container of volume `50` cc contains air (mean molecular weight =`28.8g`) and is open to atmosphere where the pressure is `100kPa`. The container is kept in a bath containing melting ice`(0^(@)C)`.(a) Find the mass of the air in the container when thermal equilibrium is reached.(b) the container is now placed in another bath containing boiling water`(100^(@)C)`. Find the mass of air in the container. (C) The container is mow closed and placed in the melting-ice bath. Find the pressure of the air when thermal equilibrium is reached .

Explanation

Given,
`(V= 50 cc. = (50 xx (10^-6)(m^3)))`
` P= 100KPa = (10^5)Pa,`
` M = 28.8 g `
` (a) PV = n(RT_1) `
` rArr PV = (m/M)(RT_1)`
` rArr m = (PMV/ RT_1)`
` = ((10^5) xx 28.8 xx 50 xx (10^-6)/ 8.3 xx 273)`
` = 50 xx 28.8 xx (10^1)/ 8.3 xx373)`
` 0.0465 gm `
(c) When the vessel is closed
` P xx 50 xx (10^-6) = (0.0465/ 28.8) xx 8.3 xx 273`
rArr P=(0.0465 xx 8.3 xx 273 / 28.8 xx 50 xx (10^-6))`
` = 0.07316 xx (10 ^6)Pa`
` = 73.16 KPa`
` = 73 KPa `