Suppose the pressure of an ideal gas mixture remains constant at 1800 Pa (1 Pa = 1 N/m2) and the temperature is increased from 220K to 1100K.
a. If the original volume of the gas was 0.17 m3, what is the final volume? (See example box 10.3.)
b. What is the change in volume ΔV for this process?
c. How much work does the gas do on the surroundings during the expansion?
d. If the initial volume was 0.24m3 and the same temperature change occurred, would the work done be the same as in the first case? Show by repeating the steps of the first three parts.
e. Is the same amount of gas involved in these two situations? Explain.
(a)
The final volume.
Answer to Problem 6SP
The final volume is
Explanation of Solution
Given info: The pressure of an ideal gas mixture is
Write the equation satisfied by idea gas at two different pressure, volume and temperature
Here,
The pressure is remains constant hence,
Rearrange equation (2) to obtain an expression for final volume
Substitute
Conclusion:
The final volume is
(b)
The change in the volume for the process.
Answer to Problem 6SP
The change in the volume for the process is
Explanation of Solution
Given info:
Write the expression for the change in volume
Substitute
Conclusion:
The change in the volume for the process is
(c)
The work done by the gas on the surroundings during the expansion.
Answer to Problem 6SP
The work done by the gas on the surroundings during the expansion is
Explanation of Solution
Given info:
Write the expression for work done in terms of volume and temperature
Here,
Substitute
Conclusion:
The work done by the gas on the surroundings during the expansion is
(d)
The work done if the initial temperature is
Answer to Problem 6SP
The final volume will be
Explanation of Solution
Given info: The initial volume is
Write the expression for final volume
Substitute
Write the expression for the change in volume
Substitute
Conclusion:
The final volume will be
(e)
To explain is the same amount of gas involved in these two situations.
Answer to Problem 6SP
The amount of gas involved in the two situations will be different.
Explanation of Solution
Given info:
Write the expression for ideal gas equation
Here,
In this case, both pressure and temperature is remains as same, but there is a change in volume. According to the above equation, the number of molecules will be different for different values of
Conclusion:
Different amount of gas will be involved in both case since, the volume is changing at constant pressure and temperature.
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