Suppose a gasfilled incandescent light bulb is manufactured

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 degree C. Find the gauge pressure inside such a bulb when it is hot, assuming its average hot temperature is 70.0 degree C. 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 beta = 2.700 Times 10^-5 degree C^-1.

Solution

According to the given problem,

Using the values given in the problem, And ideal gas equation

P₂ = P₁T₂/T₁ = 1.013*10⁵ *343.15 K / 293.15 K

P₂ = 1.1857 * 10⁵ N/m²

P_gauge = P2 - 1atm = 1.1857 * 10⁵ - 1.013 x 10^5

P_gauge = 0.173 atm

B) Using the ideal gas equation,

P_^``2 = P₂/ [1 + ß*T] = 1.173 / [1+ (2.7 * 10^-5*70)] = 1.1708

P_gauge = P_^``2 - 1atm = 1.1708 * 10⁵ - 1.013 x 10^5

P_gauge = 0.15778 atm