A. Suppose a gas-filled incandescent light bulb is manufactured so that the gas

Question

A. 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 70.0 °C.

B. 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 = 2.700 × 10-5 °C–1.

Explanation / Answer

1. COnisdering isochoric process (as volume change in buln is negligible):
P1/T1 = P2/T2
1.01*10^5/(273.16+20) = P2/(273.16+70)
P2 = 1.1822*10^5 Pa
Gauge pressure = P2 - P1 = 0.1722*10^5 Pa

B. Volume expansion coeff = 2.7*10^-5
so, New volume, V' = V(1 + 2.7*10^-5*(T2 - T1)) = V(1 + 2.7*10^-5*50) = V(1.00135)
Using P1V1/T1 = P2V2/T2
1.01*10^5*V/293.16 = P2*1.00135V/343.16
P2 = 1.18066*10^5 Pa
Gauge Pressure = 0.17066*10^5 Pa

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