Question

Two thermally insulated vessels are connected by a valve. One vessel of volume 16.8 L contains
oxygen at a temperature of 300 K and a pressure of 1.75 atm. The other vessel of volume 22.4 L
contains oxygen at a temperature of 450 K and a pressure of 2.25 atm. When the valve is
opened, the gases mix and come to equilibrium.
What is the final temperature?
What is the final pressure?

Answer 1

let μ1 ,μ2 be mole of gas rspectively then total mole of gas is

μ=μ1+μ2

since μ1=p1v1/Rt1

μ2=p2v2/Rt2

Since total mole of gas are μ

μ=P{v1+v2}/RT

then by combining all equations we get

P{V1+V2}/RT=p1v1/Rt1+p2v2/Rt2

T=t1 t2 p{V1+V2}/p1v1t2+p1v1t2

according to Boyles law

p{V1+V2}=p1v1+p2v2

then

T=T1T2{P1V1+P2V2}/P1V1T2+P2V2T1

PUT THE VALUES

T=300*450(1.75*16.8+2.25+22.4)/1.75*16.8*450+2.25*22.4*300

T=380kelwin

SAME WAY WE CAN FIND PRESSURE ALSO

P={P1V1+P2V2/T1+T2}T{V1+V2}

PUT THE VALUES

P=(1.75*16.8+2.25*22.4/300+450)380(16.8+22.4)

P=1.400atm