Suppose a gas‑filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure (1 atm=1.013×105 Pa) when the bulb has a temperature of 20.0 ∘C. Find the gauge

Question

Suppose a gas‑filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure (1 atm=1.013×105 Pa) when the bulb has a temperature of 20.0 ∘C. Find the gauge pressure inside such a bulb when it is hot, assuming its average hot temperature is 75.0 ∘C.

The actual final pressure of the light bulb will be different than calculated in the first question 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 𝛽=2.700×10−5 ∘C−1.

Answer 1

Using the ideal gas law, we can find the gauge pressure inside the bulb when it is hot:

P1V1/T1 = P2V2/T2

At 20.0 ∘C and 1 atm:

P1 = 1 atm

V1 = V2 (since the bulb is not being compressed)

T1 = 293.15 K

At 75.0 ∘C:

T2 = 348.15 K

Rearranging and solving for P2:

P2 = P1 * (T2/T1) = 1 atm * (348.15 K/293.15 K) = 1.184 atm

So the gauge pressure inside the bulb when it is hot is 0.184 atm