Incandescent lightbulbs are filled with and inert gas to lengthen the filament life. With the current off ( at t= 20.0 degrees Celsius), the gas inside a lightbulb has a pressure of 115kPa. When the bulb is burning, the temperature rises to 70.0 degrees Celsius. What is the pressure at the higher temperature?
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To find the pressure at the higher temperature, we can use Charles' Law, which states that the volume of a gas is directly proportional to its temperature, assuming constant pressure. In this case, the volume remains constant, so we can write the equation as:
(V₁/T₁) = (V₂/T₂)
Where:
V₁ = initial volume
T₁ = initial temperature
V₂ = final volume (same as initial volume, as the bulb remains the same)
T₂ = final temperature
Since the volume is constant in this case, we can rewrite the equation as:
T₁/T₂ = V₁/V₂
Now, let's plug in the known values:
T₁ = 20.0 degrees Celsius + 273.15 (convert to Kelvin) = 293.15 K
T₂ = 70.0 degrees Celsius + 273.15 (convert to Kelvin) = 343.15 K
V₁ = V₂ (constant volume)
Plugging these values into the equation:
293.15 K / 343.15 K = V₁ / V₂
Now, we know that the pressure of the gas inside the lightbulb is directly proportional to its temperature. Therefore, we can write:
(P₁/T₁) = (P₂/T₂)
Where:
P₁ = initial pressure (115 kPa)
T₁ = initial temperature (293.15 K)
P₂ = final pressure (to be determined)
T₂ = final temperature (343.15 K)
Rearranging the formula:
P₂ = (P₁ * T₂) / T₁
Now, let's substitute the known values:
P₂ = (115 kPa * 343.15 K) / 293.15 K
Calculating this equation will give us the final pressure (P₂).