Note: This problem assumes a basic understanding of an ideal gas. A cylinder wit

Question

Note: This problem assumes a basic understanding of an ideal gas. A cylinder with a diameter of 4.98 cm has a movable piston attached to a spring as shown in Figure P.40. The cylinder contains 1.41 liters of an ideal gas at 20.0°C and 1.04 atm pressure. After the gas is heated briefly and allowed to expand, it is found that the spring compresses3.42 cm and the temperature of the gas increases to 100°C.

What is the change in volume for this expansion?
mL
What is the change in pressure?
atm
What is the spring constant k?
N/m

Explanation / Answer

a)

Volume of the gas in the expansion

dV=AL=(pi*d2/4)*x

dV=(pi*0.04982/4)*0.0342

dV=6.66*10-5 m3 =66.6 cm3

dV=66.6 mL

b)

From Ideal Gas equation

P1V1/T1 = P2V2/T2

=>P2=P1*(V1/V2)(T2/T1)

P2 = 1.03*(1.41/1.41+66.6*10-3)(100+273.2/20+273.2)

P2=1.31 atm

So the change in pressure is

dP =P2-P1=1.31-1.04

dP =0.27 atm

c)

Since Work done is

W=(1/2)Kx2 =dP*dV

(1/2)*K*0.03422=(0.27*1.01325*105)*66.6*10-6

K=3115.5 N/m

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