Finding gauge pressure for gas inside light bulb as it heats up

AI Thread Summary
The gauge pressure of gas inside a light bulb as it heats up is calculated to be 0.137 atm. The formula used is P_gauge = P_f - P_i, which simplifies to P_gauge = (nR/V)(T_f - T_i) under constant volume conditions. A key piece of information is that the gas is at atmospheric pressure at 20.0°C, which helps determine the initial conditions. The participants clarify how to relate the final and initial pressures to the corresponding temperatures. The discussion concludes with an understanding of how to find the volume of gas based on this information.
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Homework Statement
Suppose a gas-filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of 20.0°C. (a) Find the gauge pressure inside such a bulb when it is hot, assuming its average temperature is 60.0°C (an approximation) and neglecting any change in volume due to thermal expansion or gas leaks. (b) The actual final pressure for the light bulb will be less than calculated in part (a) because the glass bulb will expand. Is this effect significant?
Relevant Equations
PV = nRT
For this 19(a),
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The answer is 0.137 atm.

My working is
##P_{gauge} = P_f - P_i##
##P_{gauge} = \frac{nRT_f}{V_f} - \frac{nRT_i}{V_i}##
##P_{gauge} = \frac{nRT_f}{V} - \frac{nRT_i}{V}## since volume does not change
##P_{gauge} = \frac{nR}{V}(T_f - T_i)##

However, I am not sure how to go from here since we do not know the constant volume. Does someone please know how to tackle this?

Many thanks!
 
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There is a piece of information you have not used. Can you spot it?
 
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haruspex said:
There is a piece of information you have not used. Can you spot it?
Thank you for your reply @haruspex!

No sorry, I cannot spot it.

Many thanks!
 
"the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of 20.0°C"
 
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haruspex said:
"the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of 20.0°C"
Ah, thank you for your reply @haruspex!

I see how the volume of the gas can be found now :)
 
$$\frac{P_f}{P_i}=\frac{T_f}{T_i}$$
 
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Chestermiller said:
$$\frac{P_f}{P_i}=\frac{T_f}{T_i}$$
Thank you for your reply @Chestermiller !
 
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