Question

Old question from a previous exam. Please explain how to solve.

8.) Ideal Gas (12 pts.) A cylinder with a movable piston contains 3moles of an ideal gas at an initial temperature of 250◦K and with an initial volume of 0.03m3 . 3000J of heat energy is added to the gas while the pressure of the gas is kept constant. (a) What is the final temperature of the gas? (b) What is the final volume of the gas? (c) What is the amount of work done by the gas during the expansion?

Ans:  8.) (a) 298.1K (b) 0.0358m³  (c) 1.201*10³J

Answer 1

we have formula dH = n Cp x dT where Cp of ideal gas = 5/2 R = 2.5 x 8.314 = 20.785 J/molK

dH = heat energy supplied or absorbed = 3000 J , n = moles of gas = 3 , dT = chnage in temp = T-250

now 3000 = 3 x 20.785 x ( T-250)

T = 298.1 K

c) work done = nR dT   at constant P

               = 3 x 8.314 x ( 298.1 -250)

                = 1200 J = 1.2 x 10^3 J

                      ( 1200 J = 1200x0.00987 litar atm = 11.844 liter atm)

b) work done = P x dV is another formula where P is measured from initial values using PV= nRT

initially V = 0.03 m3 = 30 liters ,

P x 30 = 3 x 0.08206 x 250     ( whre R = 0.08206 liter atm/molK)

P = 2.0515 atm

now work done = P x ( V2-V1)

11.844 = 2.0515 x ( V2-30)

V2 = 35.8 liters = 35.8/1000 m3 = 0.0358 m3