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Q. 57

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 545

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Short Answer

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:

See the step by step solution

Step by Step Solution

Step 1: Given Information (Part a)

Amount of nitrogen gas

Temperature

Initial pressure

Step 2: Explanation (Part a)

(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.

Step 3: Final Answer (Part a)

That means that the temperature will be,

Step 4: Given Information (Part b)

Amount of nitrogen gas

Temperature

Initial pressure

Step 5: Explanation (Part b)

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

Substituting the definition of as previously and we have

Multiply the values,

Step 6: Final Answer (Part b)

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

Step 7: Given Information (Part c)

Amount of nitrogen gas

Temperature

Initial pressure

Step 8: Explanation (Part c)

(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

Step 9: Final Answer (Part c)

Hence, the gas pressure after the decrease is

Step 10: Given Information (Part d)

Amount of nitrogen gas

Temperature

Initial pressure

Step 11: Explanation (Part d)

(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

Step 12: Final Answer (Part d)

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.

Step 13: Given Information (Part e)

Amount of nitrogen gas

Temperature

Initial pressure

Step 14: Explanation (Part e)

The two processes are shown in a graph below:

Step 15: Final Answer (Part e)

Therefore, the diagram is as follows:

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