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Question 2. An insulated pressure vessel divided into two parts. One part of vessel is occupiedby an ideal gas at a pressure P1, volume V1 & temp T1.The other part occupied by the same gas at a pressure P2, volume V2, & temp T2. The partition is removed and the two parts are mixed. Then show that the final pressure P3 & final T3 is

Thermodynamics 

Chapter: First law of Thermodynamics 

Question 2. An insulated pressure vessel divided into two parts. One part of vessel is occupiedby an ideal gas at a pressure P1, volume V1 & temp T1.The other part occupied by the same gas at a pressure P2, volume V2, & temp T2. The partition is removed and the two parts are mixed. Then show that the final pressure P3 & final T3 is  

Solution: 



Same ideal gas 

PV = mRT   ...................................................................(1)















Mass Conservation : m1+m2 = m3      ......................................(2)

Energy conservation: m1 u1 + m2 u2 = m3 u3 

                                     m1 Cv T1 + m2 Cv T2 = m3 Cv T3

                                m1 T1 + m2 T2 = m3 T3

Use PV =  mRT,

                P1 V1/ R + P2 V2/R = P3 V3/R

"R" Is canceled out with each other, so

P1 V1 + P2 V2 + = P3 V3

P3 = P1 V1 + P2 V2/V3 

                                                          (:: V3= V1+V2 )

P3 = P1 V1+ P2 V2/V1+V2   .............................................. (3)

Use mass conservation equation(2) and Ideal gas equation(1)

m1+ m2 = m3

P1V1/RT1 + P2V2/RT2 = P3V3/RT3

"R" is canceled out with each other because it has same value, so 

P1V1/T1 + P2V2/T2 = P3V3/T3

T3 = P3V3/ P1V1/T1 + P2V2/T2   .....................................(4)

Equation 3 and 4 are value of P3 and T3 


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