Final answer:
The gauge pressure of the gas inside the hot light bulb, assuming constant volume, is approximately 0.14 atm. This calculation does not account for the thermal expansion of the glass, which would slightly decrease the actual final pressure.
Step-by-step explanation:
To determine the gauge pressure inside an incandescent light bulb when it is hot, we can use the ideal gas law in its simplified form for a constant volume process, also known as Gay-Lussac's law. The formula we'll use is P1/T1 = P2/T2 where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature. Since the volume and the amount of gas remain constant we do not include them in our formula.
Initial conditions (P1, T1) are atmospheric pressure at 20.0°C (293.15 K), and final conditions (P2, T2) are the pressure inside the bulb when it's hot at 60.0°C (333.15 K). Atmospheric pressure is 1 atm, which equates to 1.01325 × 10µ Pa, and we are looking for the final pressure P2. The calculation is done as follows:
P2 = P1 × (T2 / T1) = 1 atm × (333.15 K / 293.15 K) = 1.136 atm. The gauge pressure will be the excess pressure above atmospheric pressure, so P2(gauge) = P2 - 1 atm = 0.136 atm or converting to a friendlier unit, P2(gauge) ≈ 0.14 atm since 1 atm is approximately 101.3 kPa.
However, when calculating the final pressure with the thermal expansion of the glass bulb, it's important to know that the bulb will expand slightly when heated, increasing the volume and therefore lowering the final pressure. This effect is typically small, but it must be considered when precision is necessary. Calculating the degree to which this occurs would require additional data not given in the question, such as the coefficient of thermal expansion for the glass material of the bulb.