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

• member 731016
In summary, the answer for 19(a) is 0.137 atm. The equation used to solve for this answer was P_gauge = (nR/V) (T_f - T_i), where the volume was found using the information that the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of 20.0°C. This was found by using the equation P_f/P_i = T_f/T_i.
member 731016
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),

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!

There is a piece of information you have not used. Can you spot it?

member 731016
haruspex said:
There is a piece of information you have not used. Can you spot it?

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"

member 731016
haruspex said:
"the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of 20.0°C"

I see how the volume of the gas can be found now :)

$$\frac{P_f}{P_i}=\frac{T_f}{T_i}$$

member 731016
Chestermiller said:
$$\frac{P_f}{P_i}=\frac{T_f}{T_i}$$

## What is gauge pressure?

Gauge pressure is the pressure of a gas or liquid measured relative to the ambient atmospheric pressure. It is the pressure reading on a gauge, which does not account for atmospheric pressure.

## How does temperature affect the pressure inside a light bulb?

As the temperature inside a light bulb increases, the gas molecules inside move faster and collide more frequently with the walls of the bulb, increasing the pressure. This relationship is described by the ideal gas law, where pressure is directly proportional to temperature.

## What is the ideal gas law and how is it used to find gauge pressure?

The ideal gas law is given by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin. To find the gauge pressure, you can rearrange the equation to solve for P and then subtract the atmospheric pressure.

## What units are commonly used for gauge pressure?

Gauge pressure is commonly measured in units such as Pascals (Pa), atmospheres (atm), pounds per square inch (psi), or bars. The choice of unit often depends on the application and the region.

## How do you measure the initial conditions of the gas inside the light bulb?

To measure the initial conditions of the gas inside the light bulb, you need to know the initial temperature and pressure of the gas before it heats up. This can be done using a thermometer for temperature and a pressure gauge for pressure. If the bulb is sealed, the initial pressure is typically assumed to be atmospheric pressure.

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