Question

The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P. Suppose that V=160 cm3 when T=320 kelvin and P=12 kg/cm2. Find the volume when T=240 kelvin and P=16 kg/cm2

Answer 1

Volume = 90 cm³

Explanation:

Given:

The volume 'V' of a fixed amount of gas is directly proportional to the temperature 'T' and inversely proportional to the pressure 'P'.

Initial volume is,
`V_1=160\ cm^3`

Initial temperature is,
`T_1=320\ K`

Initial pressure is,
`P_1=12\ kg/cm^2`

Final temperature is,
`T_2=240\ K`

Final pressure is,
`P_2=16\ kg/cm^2`

Final volume is,
`V_2=?`

As per question:

`V\propto(T)/(P)`

Therefore,

`(PV)/(T)=Constant`

Or, we can write the above as:

`(P_1V_1)/(T_1)=(P_2V_2)/(T_2)\\\\(12* 160)/(320)=(16* V_1)/(240)\\\\6=(V_1)/(15)\\\\V_1=15* 6=90\ cm^3`

Therefore, the final volume is 90 cm³.