How Does Temperature Change Affect Pressure in a Piston-Cylinder System?

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In a piston-cylinder system, warm air cools from a volume of 0.003 m^3 to 0.002 m^3 while a spring's force decreases from 900 N to 0. The atmospheric pressure is 100 kPa, and the piston area is 0.018 m^2. The ideal gas law (PV = nRT) is applicable for the air, while the spring force can be analyzed using Hooke's law (F = kx). The discussion seeks guidance on the appropriate formulas to apply for analyzing the pressure changes due to temperature variations.
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Warm air is contained in a piston-cylinder assembly cools slowly from volume of 0.003 m^3 to 0.002 m^3. During the process a spring exerts a force that varies linearly from an initial value of 900 N to final value of 0. Patm = 100 kPa and the area of the piston face is 0.018 m^2.

Or,

V1 = 0.003 m^3
V2 = 0.002 m^3

F1 = 900 N
F2 = 0

Patm = 100 kPa
Image.jpg


I'm not exactly sure where to start here. Can someone help me figure out what formula to use?
 
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PV = nRT applies to the air in the piston.
F = kx applies to the spring.
What is the question?
 

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