Q. 57

Expert-verifiedFound in: Page 545

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

of nitrogen gas at and an initial pressure of undergo an isobaric expansion until the volume has tripled.

a. What are the gas volume and temperature after the expansion?

b. How much heat energy is transferred to the gas to cause this expansion?

The gas pressure is then decreased at constant volume until the original temperature is reached.

c. What is the gas pressure after the decrease?

d. What amount of heat energy is transferred from the gas as its pressure decreases?

e. Show the total process on a diagram. Provide an appropriate scale on both axes.

a) The gas volume and temperature after the expansion is,

b) The amount of heat energy is transferred to the gas to cause this expansion is

c) The gas pressure after the decrease is

d) The amount of heat energy is transferred from the gas as its pressure decreases is

e) The total process on a diagram is as follows:

Amount of nitrogen gas

Temperature

Initial pressure

(a) Given that the volume after the expansion is three times the initial one, we just need to find the latter. From the ideal gas law, we have

Knowing that the number of molesis given as , where is the mass and is the molar mass, we have

Multiply the values,

Therefore, the volume after the expansion is

Since for an isobaric process we have const., the increase in temperature will be as many times as the increase in volume.

That means that the temperature will be,

Amount of nitrogen gas

Temperature

Initial pressure

(b) The heat exchanged in an isobaric process is given by

Substituting the definition of as previously and we have

Multiply the values,

Therefore, the amount of heat energy is transferred to the gas to cause this expansion is .

Amount of nitrogen gas

Temperature

Initial pressure

(c) For an isochoric process, we have that the ratio between the pressure and the temperature remains constant. That means, that the pressure after the second process well be decreased by just as much as the temperature.

Since the temperature has to be decreased to the level prior to the first process, this means that we have a three- time decrease. That is,

Knowing that the initial pressure was 3atm, we have

Hence, the gas pressure after the decrease is

Amount of nitrogen gas

Temperature

Initial pressure

(d) In an isochoric process the heat exchanged is given by

Substituting just as in (b), with the difference that the temperature change here is negative, we have

Therefore, amount of heat energy is transferred from the gas as its pressure decreases is The negative sign is an indicator that the heat was released by the gas.

Amount of nitrogen gas

Temperature

Initial pressure

The two processes are shown in a graph below:

Therefore, the diagram is as follows:

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