A cylinder that has a 45.0-cm radius and is 50.0 cm deep is filled with air at 2

Question

A cylinder that has a 45.0-cm radius and is 50.0 cm deep is filled with air at 28.0°C and 1.00 atm shown in figure (a). A 16.0-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 20.5-kg dog stands on the piston, further compressing the air, which remains at 28.0°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

(A) (Pin - Patm) A = m g

( P inside - 101325) ( pi 0.45^2) = (16 x 9.8)

P inside = 101571 Pa

now, P' - 101325 = ((16 + 20.5)(9.81) ) / (pi 0.45^2)

P' = 101886 Pa

P V = P' V'

101571 ( hi A) = (101886) (h' A)

h' = 1.003113 hi

for hi, PV / T = constant

(101325) (50 A) / (T) = (101571) (hi A) / T

hi = 49.8789 cm

deltah = (1.003113 - 1)(49.8789) = 0.155 cm = 1.55 mm ......Ans

(b) V / T = constant

( A x (49.8789 - 0.155)) / (273 + 28) = ( A x 49.8789) / T

T = 301.94 K Or 28.9 deg C

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