The pressure exerted by `12 g` of an ideal gas at temperature `t^(@)C` in a vessel of volume `V litre` is `1 atm`. When the temperature is increased by `10^(@)C` at the same volume, the pressure increases by `10%`. Calculate the temperature `t` and volume `V`. (Molecular weight of the gas is `120`).

Explanation

Case I Given `P = 1 atm, w = 12 g ,T = (t + 273) K,`
`V =V litre`
Case II `T = (t + 283) K, P = 1 + (10)/(100) = 1.1 atm, w = 12 g`
`V =V `litre
Using gas equation
Case I ` 1 xx V = (12)/(m) xx R (t + 273)`
Case II `1.1 xx V =(12)/(m) xx R (t +2283)...(2)`
By eps (1) and (2)
`(1.1)/(1) = (t + 283)/(t + 273)` ltbr gt`:. 1.1t + 300.3 = t + 283`
`:. 0.1t = - 17.3`
`:. t = - 173^(@)C =100 K` .
Also from case I
`1 xx V = (12)/(120) xx 0.082 xx 100 ( :' m = 120)`
`V = 0.82` litre