A diatomic ideal gas has an initial pressure of 200 Pa, at an initial volume of

Question

A diatomic ideal gas has an initial pressure of 200 Pa, at an initial volume of 0.0125 m^3 and the initial temperature is 300 K, thus you have 0.001 moles. Assume that the molecules can rotate, but not vibrate. The system completes one full cycle, a rightarrow b rightarrow c rightarrow a. Obtain the work from a rightarrow b. Obtain the work from b rightarrow c. Obtain the change in internal energy from a rightarrow b. Obtain the heat added from a rightarrow b. Obtain the efficiency of this engine.

Explanation / Answer

Here ,
a)

for a to b

work done = area under the curve

work done = (0.0250 - 0.0125)* 150 + (0.0250 - 0.0125) * 0.5 * (200 - 150)

work done = 2.19 J

the work done a to b us 2.19 J

b)

for b to c

work done = - (0.0250 - 0.0125) * 150

work done = -1.875 J

work done from b to c is -1.875 J

c)

at a

P * V = n * R * Ta

200 * 0.0125 = 0.001 * 8.314 * Ta

Ta = 300.7 K

at b

150 * 0.0250 = 0.001 * 8.314 * Tb

Tb = 450 K

change in internal energy = 1.5 * n * R *(Tb - Ta)

change in internal energy = 1.5 * 0.001 *8.314 (449.6 - 300.7)

change in internal energy = 1.86 J

the change in internal energy is 1.86 J

d)

heat added from a to b = Uab - Wab

heat added from a to b = - 2.19 + 1.86

heat added from a to b = -0.33 J

the heat added from a to b is -0.33 J

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