Model air as a diatomic ideal gas with M = 28.9 g/mol. A cylinder with a piston contains 1.20 kg of air at 25.0°C and 2.00 × 105 Pa. Energy is transferred by heat into the system as it is permitted to expand, with the pressure rising to 4.00 × 105 Pa. Throughout the expansion, the relationship between pressure and volume is given by P = CV1/2 where C is a constant. Find (a) the initial volume, (b) the final volume, (c) the final temperature, (d) the work done on the air, and (e) the energy transferred by heat.
(a)
The initial volume.
Answer to Problem 21.55AP
The initial volume is
Explanation of Solution
Given info: Molar mass is
Write the expression for ideal gas equation.
Here,
Reaarange above equation for
Write the expression for number of moles of gas.
Here,
Substitute
Thus, the number of moles of gas is
Substitute
Conclusion:
Therefore, the initial volume is
(b)
The final volume.
Answer to Problem 21.55AP
The final volume is
Explanation of Solution
Given info: Molar mass is
Write the expression for the relationship between pressure and volume for adiabatic process for an ideal gas:
Rearrange equation (4) for
Square both side in above equation.
Substitute
Conclusion:
Therefore, final volume is
(c)
The final temperature.
Answer to Problem 21.55AP
The final temperature is
Explanation of Solution
Given info: Molar mass is
Write the expression for ideal gas equation.
Here,
Rearrange above equation for
Substitute
Conclusion:
Therefore, the final temperature is
(d)
The workdone on the air.
Answer to Problem 21.55AP
The work done on the air is
Explanation of Solution
Given info: Molar mass is
Write the expression for work done.
Here,
Write the expression for relationship between pressure and volume:
Here,
Rewrite above expression for
Substitute
Substitute
Substitute
Conclusion:
Therefore, the work done on the air is
(e)
The energy transferred by heat.
Answer to Problem 21.55AP
The energy transferred as heat is
Explanation of Solution
Given info: Molar mass is
The molar specific heat at constant pressure is,
Write the expression for change in internal energy.
Here,
Substitute
Here,
Substitute
Thus, the change in internal energy is
Write the expression for the energy transferred as heat.
Here,
Substitute
Conclusion:
Therefore, the energy transferred as heat is
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Chapter 21 Solutions
Physics for Scientists and Engineers, Technology Update, Hybrid Edition (with Enhanced WebAssign Multi-Term LOE Printed Access Card for Physics)
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