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 degreeC. Find the gauge pressure inside such a bulb when it is hot, assuming its average hot temperature is 65.0 degreeC. 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 = 2.700 times 10^5 degreeC^_1.

Explanation / Answer

Here ,

T1 = 20 degree C = 293 K

P1 = 1 atm

P2 = ?

T2 = 65 degree C = 338 K

for the ideal gas equation

P1/T1 = P2/T2

1/293 = P2/338

P2 = 1.153 atm

final gauge pressure = P2 - Pa

final gauge pressure = 1.153 - 1

final gauge pressure = 0.153 atm

final gauge pressure = 0.153 * 1.01 *10^5

final gauge pressure = 15512 Pa

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for the final volume

v2 = v1 * (1 + B * delta T)

v2 = v1 * (1 + 2.7 *10^-5 * 45)

v2 = 1.001215 * v1

Using ideal gas law

P1* V1/T1 = P2* V2/T2

1 * 1 /293 = P2 * 1.001215/338

P2 = 1.152 atm

final gauge pressure = P2 - Pa

final gauge pressure = 1.152 - 1

final gauge pressure = 0.152 atm

final gauge pressure = 0.152 * 1.01 *10^5

final gauge pressure = 15370.6 Pa

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