Question

Suppose a gas-filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure (absolute pressure) when the bulb has a temperature of 18.1°C. (Enter your answers to at least four significant figures.)

(a) Find the gauge pressure inside such a bulb in atmospheres when it is hot, assuming its average temperature is 57.0°C(an approximation) and neglecting any change in volume due to thermal expansion or gas leaks.

(b) The actual final pressure for the light bulb will be less than calculated in part (a) because the glass bulb will expand. What will the actual final gauge pressure be in atmospheres, taking this into account?

Answer 1

Answer :

(a) When the volume is constant: P/T = constant.
P₁/T₁ = P₂/T₂
P₂ = P₁T₂ / T₁ = 101.325kPa*57°C / 18.1°C = 320.86 kPa <------------

b) Volume expansion: ∆V = βV∆T
∆V/V = β∆T = 9×10 ̄ ⁶C ̄ ¹ * 38.9°C = 3.5×10 ̄ ⁴, which means the bulb expands by 0.035%

Using the gas law to determine ratios: PV = nRT => PV/T = constant
P₁V₁/T₁ = P₂V₂/T₂
P₂ = P₁V₁T₂ / V₂T₁ = P₁V₁T₂ / 1.00035V₁T₁ = P₁T₂ / 1.00035T₁
P₂ = 303.98kPa / 1.00035 = 320.75 kPa <-------------

The difference between this value and the value from part (a) is negligible