Final answer:
Using Gay-Lussac's law for the proportional relationship between pressure and temperature of a gas at constant volume, the gauge pressure was calculated to be 112.4 kPa when the bulb is heated to 350.0ºC, starting from atmospheric pressure at 20.0ºC.
Step-by-step explanation:
Calculating the Gauge Pressure in a Hot Incandescent Bulb
To calculate the gauge pressure of a gas-filled incandescent light bulb when heated to 350.0ºC from an initial temperature of 20.0ºC, we will use the ideal gas law and the concept of gauge pressure. The initial condition is at atmospheric pressure, which equates to a gauge pressure of 0 kPa, as gauge pressure is the difference between absolute pressure and atmospheric pressure.
Assuming ideal gas behavior, the pressure change due to temperature can be calculated using Gay-Lussac's law, which states that P1/T1 = P2/T2 where P is the pressure, and T is the temperature in kelvins. First, we need to convert the temperatures from Celsius to Kelvin by adding 273.15.
Initial temperature (T1) = 20.0ºC + 273.15 = 293.15 K
Final temperature (T2) = 350.0ºC + 273.15 = 623.15 K
Because the initial condition is at atmospheric pressure, the initial absolute pressure (P1) is about 101.3 kPa (standard atmospheric pressure). Using Gay-Lussac's law and rearranging for P2 gives us:
P2 = P1 * (T2 / T1) = 101.3 kPa * (623.15 K / 293.15 K) = 213.7 kPa
To find the gauge pressure, which is the result we're seeking, we subtract the atmospheric pressure from this result:
Gauge Pressure = P2 - Atmospheric Pressure = 213.7 kPa - 101.3 kPa = 112.4 kPa
Looking at the provided options, none of them match the calculated value of 112.4 kPa. Please check the temperature or conditions provided, as they might affect the calculations.