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

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

Comments

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Question 1. A spherical balloon of 1m diameter contains a gas at 150kpa. The gas inside balloon is heated until pressure reaches 459kpa. During the process of heating the pressure of gas inside the balloon is proportional to cube of the diameter of the balloon. Find the work done by the gas.