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 °C. Find the gauge pressure inside such a bulb when it is hot, assuming its average hot temperature is 65.0 °C Number 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 B-2.700 x10 °C-1 Number Pa

Answer 1

When the volume is constant: P/T = constant.
P₁/T₁ = P₂/T₂

p1=101325Pa (atmospheric)
P₂ = P₁T₂ / T₁ = 101325Pa*65°C / 20°C = 329306.25 Pa <------------ answer

b) Volume expansion: ∆V = βV∆T
∆V/V = β∆T = 2.7*10^-5C ̄ ¹ * 45°C = 21.5×10 ̄ ⁴, which means the bulb expands by 0.215%

Using the gas law to determine ratios: PV = nRT => PV/T = constant
P₁V₁/T₁ = P₂V₂/T₂
P₂ = P₁V₁T₂ / V₂T₁ = P₁V₁T₂ / 1.00215V₁T₁ = P₁T₂ / 1.00215T₁
P₂ = 329306.25 Pa / 1.00215= 328485Pa <---answer