A cylinder with a movable piston contains 17 moles of a monatomic ideal gas at a

Question

A cylinder with a movable piston contains 17 moles of a monatomic ideal gas at a pressure of 1.45 × 10^5 Pa. The gas is initially at a temperature of 300 K. An electric heater adds 44500 J of energy into the gas while the piston moves in such a way that the pressure remains constant. It may help you to recall that Cp = 20.79 J/K/mole for a monatomic ideal gas, and that the number of gas molecules is equal to Avagadros number (6.022 × 10^23) times the number of moles of the gas.

1) What is the temperature of the gas after the energy is added?

2) What is the change in volume of the gas?

3)How much work is done by the gas during this process?

Explanation / Answer

1)
dQ = n*Cp*dT
Tf= T0 + q/nCp
Tf= 300 + 44500/17*20.79
Tf= 426K

2)
P1*V1 = n*R*T1
1.45x10^5*v1=17*8.314*300
V1= 17*8.314*300/1.45x10^5
V1= 0.292 m^3

after heat is added

P1*V2 = n*R*T2
1.45x10^5*v2=17*8.314*426
V2= 17*8.314*426/1.45x10^5
V2= 0.415 m^3

dV = v2 - v1 = 0.123 m^3

3)
W= PaT= 1.45×10^5*0.123= 17835J

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