Final answer:
The gauge pressure in a gas-filled incandescent light bulb that is hot can be estimated using the Ideal Gas Law, which equates the ratio of pressure to temperature at one state to that at another state. This calculation assumes that the volume of the gas and amount are constant. However, in reality, the glass expands when heated, meaning the actual pressure would be slightly less than the theoretical gauge pressure.
Step-by-step explanation:
To calculate the gauge pressure inside a hot gas-filled incandescent light bulb, we need to use the Ideal Gas Law, which states that the pressure of a gas is directly proportional to its temperature if the volume and the amount of gas remain constant (represented as P/T = constant). Since the gas inside the bulb is at atmospheric pressure at 20.0°C, we need to find the pressure at the new temperature, which is 75.0°C in this scenario. It is important to note that this calculation is a theoretical one, assuming the volume of the gas does not change when heating up, which is not entirely accurate because the glass will expand slightly. The actual final pressure will thus be a bit lower than the calculated gauge pressure.
Using the Ideal Gas Law formula:
P1/T1 = P2/T2 (where P is pressure and T is temperature in kelvins)
Convert temperatures from Celsius to Kelvin by adding 273.15
Assuming atmospheric pressure at 20.0°C is 1.00 atm and the temperature is 293.15 K, and the hot temperature is 348.15 K (75.0°C in kelvins)
Solve for P2 to find the gauge pressure at 75.0°C
This estimation, however, will not account for the real-life scenario where the glass expands and hence the actual final pressure will be lower than the gauge pressure calculated with the ideal conditions assumed.