Final answer:
To find the gauge pressure inside the gas-filled incandescent light bulb when it is hot, we can use the ideal gas law and the given temperatures to calculate the final pressure. Neglecting any change in volume due to thermal expansion or gas leaks, the final pressure would be the same as the initial atmospheric pressure.
Step-by-step explanation:
To find the gauge pressure inside the gas-filled incandescent light bulb when it is hot, we can use the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature.
Since the bulb is filled with gas at atmospheric pressure when its temperature is 20.0°C, we can find the initial pressure. Then, using the average temperature of 65.0°C, we can calculate the gauge pressure by subtracting atmospheric pressure from the final pressure.
If we neglect any change in volume due to thermal expansion or gas leaks, the final pressure inside the bulb would be the same as the initial pressure, which is atmospheric pressure.
To find the gauge pressure inside an incandescent light bulb at an elevated temperature of 60.0°C, the Ideal Gas Law is used, which reveals an increase in pressure. The effect of the bulb's thermal expansion would lead to a decrease in pressure, and this could be a significant factor affecting both design and operation.
The question involves calculating the gauge pressure of a gas inside an incandescent light bulb when it is heated from its manufacturing temperature. This is a classic application of the Ideal Gas Law, which can be simplified in this case due to the assumption of constant volume and no leaks.
Finding the Gauge Pressure
To find the gauge pressure inside the bulb at 60.0°C, we can apply the Ideal Gas Law in the form of the combined gas law, which states that for a given mass of an enclosed gas, the ratio of the product of pressure and volume to temperature remains constant (P1V1/T1 = P2V2/T2). We can simplify this to P1/T1 = P2/T2 as the volume is constant.
Atmospheric pressure at 20.0°C (assumed to be the initial condition) is 1 atm. Converting the temperatures to Kelvin, we get T1 = 293.15 K and T2 = 333.15 K. The final pressure P2 is what we want to find:
P2 = P1 * (T2/T1)
P2 = 1 atm * (333.15 K / 293.15 K)
P2 is therefore higher than 1 atm. To express this in more common units, 1 atm is equivalent to 101325 N/m². Thus, the gauge pressure can be calculated and will be expressed in N/m² (Pascals).
This increase in pressure when the bulb is hot can impact the durability and function of the light bulb, making it a significant factor in the design and operation of incandescent bulbs.
Considering Thermal Expansion
The second part of the question addresses the impact of thermal expansion of the glass bulb on the final pressure. If the glass expands, the volume of the bulb increases, and according to the Ideal Gas Law, for a given mass of gas, if the volume goes up, the pressure would decrease assuming all other factors remain constant.
Even with a smaller increase in pressure due to the bulb's expansion, the difference may be non-negligible, depending on the materials' thermal expansion coefficient and bulb design.