A cylinder with a movable piston contains 18.9 moles of a monatomic ideal gas at

Question

A cylinder with a movable piston contains 18.9 moles of a monatomic ideal gas at a pressure of 2.21 × 105 Pa. The gas is initially at a temperature of 300 K. An electric heater adds 52100 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?

2.

What is the change in volume of the gas?

3.

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

Explanation / Answer

Number of moles n = 18.9 mol

Initial pressure P = 2.21 x10 5 Pa

Initial temprature T = 300 K

Initial volume V = nRT / P

                       = 18.9(8.314)(300)/(2.21x10 5)

                       = 0.2133 m 3

Energy added Q = 52100 J

We know Q = nCp(T ' - T )

     52100= 18.9(20.79)(T ' -300)

     T ' - 300 = 132.59

             T ' = 432.59 K

(2). At constant pressure ,V ' /V = T ' / T

            V ' = (T ' /T ) V

                 = (432.59/300) 0.2133

                 = 0.3075 m 3

Change in volume =V ' - V

                           = 0.3075 -0.2133

                           = 0.09427 m 3

(3).Work done W = P(V '-V)

                          = 2.21 x10 5 x0.09427

                          = 20.835 x10 3 J

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