A cylinder with a movable piston contains 15.2 moles of a monatomic ideal gas at
ID: 1485849 • Letter: A
Question
A cylinder with a movable piston contains 15.2 moles of a monatomic ideal gas at a pressure of 2.74 × 105 Pa. The gas is initially at a temperature of 300 K. An electric heater adds 57400 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 × 1023) times the number of moles of the gas. 1) What is the temperature of the gas after the energy is added? K Submit 2) What is the change in volume of the gas? m3 Submit 3) How much work is done by the gas during this process?
Explanation / Answer
1)
dQ = n*Cp*dT
57400 = 15.2*20.79*dT
dT = 181.64 K
T2 - T1 = 181.64
T2 - 300 = 181.64
T2 = 481.64 K
+++
2)
P1*V1 = n*R*T1
2.74*10^5*V1 = 15.2*8.314*300
V1 = 0.138 m^3
after heat is added
P1*V2 = n*R*T2
2.74*10^5*V1 = 15.2*8.314*481.64
v2 = 0.222 m^3
dV = v2 - v1 = 0.084 m^3 <<-answer
+
3)
W = P*dV = 2.74*10^5*0.084 = 23016 J
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