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 average hot temperature is 75.0 degree C. Pa The actual final pressure of the light bulb will be different than calculated above because the glass bulb will expand. What will the final actual gauge pressure be, taking this into account? The volume expansion coefficient for glass is beta = 2.700 times 10^-5 degree C^-1. Pa

Explanation / Answer

Assuming volume constant then

P1 / T1 = P2 / T2

1 atm / (273 + 20) = P / (273 + 75)

P = 1.188 atn

Gauge pressure = P - P_atm = 0.188 atm Or 0.188 x 101325 Pa

Ans: 19020 Pa
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V = Vo (1 + alpha deltaT )

V = V0 (1 + (2.7 x 10^-5)(75-20)) = 1.001485 V0

Applying P1 V1 / T1 = P2 V2 / T2

(1 atm) (V0) / (273 + 20) = P (1.001485 V0) / (273 + 75)

P = 1.186 atm

Gauge pressire = 1.186 - 1 = 0.186 atm

In Pa = 18841 .6 Pa

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