A VERTICAL CYLINDER CLOSED AT BOTH ENDS IS DIVIDED INTO TWO PARTS INTO TWO FRICTIONLESS PISTON EACH PART CONTAINING ONE - Chemistry - States of Matter

Question

A VERTICAL CYLINDER CLOSED AT BOTH ENDS IS DIVIDED INTO TWO PARTS
INTO TWO FRICTIONLESS PISTON EACH PART CONTAINING ONE MOLE OF AIR
AT TEMPERATURE 300K, THE VOLUME OF UPPER PART IS 4TIMES THAN THAT
OF THE LOWER PART AT WHAT TEMPERATURE WILL THE VOLUME OF THE UPPER
PART BE THREE TIMES THAN THAT OF THE LOWER PART?

Vartika Jain · Accepted Answer

Dear Student,

P2=Pt+P1PV=nRTor, P=nRTVor, nRTV2=nRTV1+Ppr, P=nRT(1V2-1V1)and, V=V1+V2When V1=aV2                 V=V2(a+1)or, V2=Va+1SImilalry, V2=1a+1V1or, V=1a+1V1+V1or, V=V1+1aor, nRT(1+aV-1+1aV) =Pn=1RT1V(a-1a)=Por, RT1V(a1-1a1)= P  and RT2V(a2-1a2)= PLet total pressure, P be 1 thenT2T1×(a2-1a2)(a1-1a1)=1T2300×(3-13)(4-14)=1T2300×(83)(154)=1T2300×83×415=1or, T2=4532×300=421
87 K