Question

Suppose a gas-filled incandescent light bulb is manufactured from regular glass and with atmospheric pressure in it at 20.00°C. Its average temperature when hot is 63.51°C. Neglecting any change in volume due to thermal expansion or gas leaks, its gauge pressure is calculated to be 0.1485 atm. The actual final pressure for the light bulb will be less than calculated because the glass bulb will expand. What will the actual final gauge pressure be, taking this into account? The coefficient of volume expansion for regular glass is 27 ✕ 10⁻⁶/°C. (Give your answer to at least four decimal places.)

Answer 1

As we know that

a) When the volume is constant: P/T = constant.
P₁/T₁ = P₂/T₂
P₂ = P₁T₂ / T₁ = 49.142625kPa*63.51°C / 20°C = 156.0524057 kPa

b) Volume expansion: ∆V = βV∆T
∆V/V = β∆T = 27×10 ̄ ⁶C ̄ ¹ * 43.51°C = 1.17477×10 ̄ ⁴

Using the gas law to determine ratios: PV = nRT => PV/T = constant
P₁V₁/T₁ = P₂V₂/T₂
P₂ = P₁V₁T₂ / V₂T₁ = P₁V₁T₂ / 1.0001174V₁T₁ = P₁T₂ / 1.0001174T₁
P₂ = 156.0524057kPa / 1.000117477 = 156.0340753 kPa

The difference is almost neglible.