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A piston–cylinder assembly fitted with a slowly rotating paddle wheel contains 0.17 kg of air, initially at 300 K. The air undergoes a constant-pressure process to a final temperature of 400 K. During the process, energy is gradually transferred to the air by heat transfer in the amount 12 kJ.Assuming the ideal gas model with k = 1.4 and negligible changes in kinetic and potential energy for the air, determine the work done by the paddle wheel on the air and by the air to displace the piston, each in kJ.

Question

A piston–cylinder assembly fitted with a slowly rotating paddle wheel contains 0.17 kg of air, initially at 300 K. The air undergoes a constant-pressure process to a final temperature of 400 K. During the process, energy is gradually transferred to the air by heat transfer in the amount 12 kJ.

Assuming the ideal gas model with k = 1.4 and negligible changes in kinetic and potential energy for the air, determine the work done by the paddle wheel on the air and by the air to displace the piston, each in kJ.

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Step 1

Assumption:

Air as ideal gas
Consider air in the piston- cylinder assembly is the closed system.
Change in kinetic and potential energies are negligible
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Air as ideal gas Consider air in the piston- cylinder assembly is the closed system. Change in kinetic and potential energies are negligible

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Step 2

Calculate the work done at the air –piston interface.

— P(", - и)
W
piston
= mR(T, -T
8.314 kJ
(400 -300)K
=0.17 kg x
28.47 kg K
-4.9645 kJ
Thus, the work done by the air to displace the piston is 4.9645 kJ.
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— P(", - и) W piston = mR(T, -T 8.314 kJ (400 -300)K =0.17 kg x 28.47 kg K -4.9645 kJ Thus, the work done by the air to displace the piston is 4.9645 kJ.

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Step 3

Write the energy bala...

AUAKE APE = Q- W
W
Q - AU
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AUAKE APE = Q- W W Q - AU

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