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.

THERMODYNAMICS QUESTION SOLUTION,

CHAPTER. ENERGY INTERACTION.

Question 1. A spherical balloon of 1m diameter contains a gas at 150 KPa. The gas inside balloon is heated until pressure reaches 450 KPa. 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.

Solution: D1= 1 m   

P1= 150 KPa                                           V = (4/3) π R^3 =  πD^3/6      

P2 = 450 KPa                                             dV = (π/6)  (3D^2)  δD

P directly proportional D^3                         dV = (π/2) (D^2)  δD

P = k(D^3)                                                  W = ∫ P dV  --------------(0)

P1=k(D1^3)                                                

150 = k(1)^3                                             

k = 150 KN/m^3 ----------------(1)               

P2 = k(D2^3)

450 = 150(D2)^3

D2 = 1.44 m -----------------------(2)

W = ∫ P dV

 W = ∫ (kD^3) (π/2) (D^2)  δD

  W = kπ/2  ∫ (D^5) δD

                                 D2

  W = kπ/2 [D^6/6]

                               D1

W = kπ/12 [D2^6 - D1^6]

W = 150(3.14)/12 [ (1.44)^6 - (1)^6]

W = 312  m^6 (KN/m^5)

W = 312  KN.m = 312 KJ     ------------------------------------(3)