A cylinder that has a 38.5-cm radius and is 50.0 cm deep is filled with air at 1

Question

A cylinder that has a 38.5-cm radius and is 50.0 cm deep is filled with air at 11.5°C and 1.00 atm shown in figure (a). A 15.0-kg piston is now lowered into the cylinder, compressing the air trapped inside as it takes equilibrium height hi as shown in figure (b). Finally, a 27.5-kg dog stands on the piston, further compressing the air, which remains at 11.5°C as shown in figure (c).

(a) How far down (h) does the piston move when the dog steps onto it?
mm

(b) To what temperature should the gas be warmed to raise the piston and the dog back to hi?
°C

Explanation / Answer

T = cosntant

PV = Po*Vo

V = Ah

A = cosntant

P = Po(ho/hi)

P = Po +mg/A

hi = ho/[1+(mg/Po*A)]

wit hthe dog mass m on the piston

h' = ho/[1+(m+M)g/PoA]

dh = hi - h'

ho = 50 cm =

A =pi*0.385^2

m = 15 kg

M = 27.5 kg

dh = 0.2823 cm = 2.823 mm

part b )

P =cosntant

V/T = V'/Ti

Ahi/T = Ah'/Ti

T = Ti(hi/h')

Ti = 11.5 c = 284.5 K

T = 286.12 K = 13.12 C

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