3. A sample of a monatomic ideal gas is taken through the cyclic process abca sh

Question

3. A sample of a monatomic ideal gas is taken through the cyclic process abca shown in the figure below. The values along the pressure axis are pb = 7.50 kPa and pac = 2.50 kPa. The values along the volume axis are Va = 1.00 m3 and Vbc = 3.00 m3 . The temperature at state a is Ta = 200 K. (a) How many moles of gas are in the sample? (b) What is the temperature of the gas at point b? (c) What is the temperature of the gas at point c? (d) What is the net energy added to the gas as heat along each step in the cycle and over the entire cycle?

Explanation / Answer

FROM THE EQN WE HAVE

Pb Vb Tb = RTa-------(1)

(7.50x10^3)(3)(Tb) = 8.31(200)

Tb = 346k at the point b

again we have the equation

Pa Va Ta = R Tc

Tc = (2.50x10^3)(200) / 8.31

Tc = 333k at the point c

since it is a monoatomic gas there are 3 degrees of freedom

so m = 3

energy is given by the eqn

E = 1/2 m [ V^2a +V^2bc]

   = (0.5)(3)[1^2+ 3^2]

E= 15J

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