A cylinder that has a 37.0-cm radius and is 50.0 cm deep is filled with air at 2

Question

A cylinder that has a 37.0-cm radius and is 50.0 cm deep is filled with air at 29.5 degree C and 1.00 atm shown in figure (a). A 22.0-kg piston is now lowered into the cylinder, compressing the air trapped inside as it takes equilibrium height h as shown in figure (b). Finally, a 21.0-kg dog stands on the piston, further compressing the air, which remains at 29.5?C as shown in figure (c). (a) How far down (triangle 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? [ ]degree C

Explanation / Answer

Here ,

pressure when piston is kept ,

P1 = Pa + 22*9.8/(pi*.37^2)

P1 = 1.015 *10^5 Pa

Now, when the dog steps on

P2 = P1 + 21*9.8/(pi*.37^2)

P2 = 1.0198 *10^5 Pa

Now, Uisng boyle law

50 * A * 1.01 *10^5 = hi * A * 1.015 *10^5

hi = 49.754 cm

Now , again using boyle law

(hi - del h ) * 1.0198 * 10^5 * A = hi * A * 1.015 *10^5

del h = 4.71 *10^-3 * 49.754

del h = 0.234 cm

del h = 2.34 mm

b)

Now, T1 = 29.5 C = 302.5 K

Using ideal gas law , under costant pressure ,

302.5/A*(49.754 -0.234 ) = T2/(49.754)*A

302.5/(49.754 -0.234 ) = T2/(49.754)

solving for T2

T2 = 303.93 K = 30.3 degree C

the temperature is 30.3 degree C

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