A cylinder that has a 40.5-cm radius and is 50.0 cm deep is filled with air at 1

Question

A cylinder that has a 40.5-cm radius and is 50.0 cm deep is filled with air at 18.0°C and 1.00 atm shown in figure (a). A16.0-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 22.0-kg dog stands on the piston, further compressing the air, which remains at 18.0°C as shown in figure (c).

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

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

Explanation / Answer

initially

P(50 A) = (P+16*9.8/A ) hiA

10^5 (50) = 100304.2 ( hi)

hi = 49.8483

b)

we know that

if pressure constant

V1/T1 = V2/T2

V2/V1 = T2/T1

V2 = = A(hi-deltah)= ( 49.64)A

V1 = A 49.8483

substituting

0.99586 = 18+273 /T

T = 292.20 k

T = 19.208 C

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