A vertical piston - cylinder assembly contains 0.050 m3 of a gas at 1.0 bar. The

Question

A vertical piston - cylinder assembly contains 0.050 m3 of a gas at 1.0 bar. The piston is restrained by a linear spring as well as the atmosphere. Initially, the atmospheric pressure of 1.0 bar just balances the gas pressure, and the spring exerts no force on the piston. (Neglect the weight of the piston). The gas is now heated quasistatically until its volume and pressure are 0.080 m3 and 1.9 bars, respectively

Develop an equation for the relationship between the pressure and the volume of the gas, with the pressure in N/m2 and the volume in cubic meter

Explanation / Answer

Inittially

force by piston,F = 0

P gas = Patm + F/A

F=kx(linear spring)

= k(Vgas- V initial)/A

P = Patm +  k(Vgas- V initial)/A2

P= 1x 105 + k/A2 (V- 0.05)

 

subst values of P and V as 0.080 m3 and 1.9 bars, to find k/A2

1.9 bar= 1 bar+ K' (0.03)

k' =30 x 105

p =105 + 30x105 (V-0.05)

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