A cylinder with a movable piston contains 13.7 moles of a monatomic ideal gas at

Question

A cylinder with a movable piston contains 13.7 moles of a monatomic ideal gas at a pressure of 2.15 × 105 Pa. The gas is initially at a temperature of 300 K. An electric heater adds 51500 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

2)

What is the change in volume of the gas?

m3

3)

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

J

Explanation / Answer

n = number of moles = 13.7 moles

P1 = initial pressure = 2.15 × 105 Pa

V1= initial Volume

T1 = temperature = 300 K

using the formula

P1 V1 = n R T1

(2.15 × 105 ) V1 = (13.7) (8.314) (300)

V1 = 0.16 m3

T2 = temperature after heat is added

Q = heat = 51500 J

Using the formula

Q = n Cp (T2 - T1) = 13.7 (20.79) (T2 - 300)

51500 = 13.7 (20.79) (T2 - 300)

T2 = 480.8

Using

the formula

V1 /T1 = V2/T2

0.16 / 300 = V2 / 480.8

V2 = 0.26 m3

work done = P (V2 - V1) = (2.15 × 105 ) (0.26 - 0.16) = 21500 J

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