Suppose a gas-filled incandescent light bulb is manufactured so that the gas ins

Question

Suppose a gas-filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of 20.0 degree C. Find the gauge pressure inside such a bulb when it is hot, assuming its averaging hot temperature is 70.0 degree C. the actual final pressure of the light bulb will be different that calculated above because the glass bulb will expand. what will the final actual gauge pressure be, taking this into account? The volume expansion coefficient ofr glass is beta = 2.700*10^-5 C^-1.

Explanation / Answer

a)
The volume is constant here, so the pressure will increase with increase in temperature.
T1 = 20 deg C = 293 K
T2 = 70 deg C = 343 K
P1 = 101325 pa
P2 = P1*T2/T1 = 101325*343/293=118615.96 pa
The gauge pressure = 118615.96 pa - 101325 pa = 1.729*10^4 Pa
b)
T1 = 20 deg C = 293 K
T2 = 70 deg C = 343 K
P1 = 101325 pa
V2 = V1*beta*delta T = V1*2.7*10^-5*50
V2 = V1*135*10^-5
So from ideal gas equation,
P1V1/T1 = P2V2/T2
P2 = 101325*(V1/V2)*(T2/T1) = 101325*740.74*343/293 = 87863583 pa
guage pressure = 87762258 pa

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