# What is the surface area of the filament? heat expansion and transfer

• teggenspiller
In summary, the filament of a light bulb has a temperature of 2580C and radiates 60W of power. The emissivity of the filament is 0.36. The surface area of the filament is 144mm^2.
teggenspiller

## Homework Statement

the filament of a light bulb has a temperature of 2580Cel. and radiates 60W of power. The emissivity of the filament is 0.36. What is the surface area of the filament?

## Homework Equations

P= $$\sigma$$*A*emissivity*T^4

A=?
$$\sigma$$=$$\sigma\ =\ 5.670400(40)\ \times\ 10^{-8}\ W\ ^{-2}\ K^{-4}$$
T=2580C and for this equation we need to use the absolute K temp, which is 2580+273, so it is 2583K
P=60, so set the equation to 60
and e= .36

## The Attempt at a Solution

60W=A*$$\sigma\ =\ 5.670400(40)\ \times\ 10^{-8}\ W\ ^{-2}\ K^{-4}$$*(.36)*(2583 ^4)

and when I solve for A i get hugely long decimals (obviously), by dividing 60 by this huge number. the multiple choice answers are

a)44mm^2
b) 62
c) 74
d) 91
3) 144

all in mm^2

Well, for one thing 2580+273 is 2853, not 2583. For another your units on sigma are wrong. But most importantly, yes, you get a rather small number. What do you get? But that's the area in m^2. How many mm^2 in a m^2?

wait, how are they wrong? its what physics forums gave me?

teggenspiller said:
wait, how are they wrong? its what physics forums gave me?

Did they?? Then that would be wrong. If you want sigma*emissivity*A*T^4 to come out in watts then sigma should have units W/(m^2*K^4). But that's not the important part for your problem. How many m^2 do you get?? A small number in units of m^2 is a large number in mm^2.

yes but i am getting 1.8*10^12 in Meters, and its not an option when converted to mm

teggenspiller said:
yes but i am getting 1.8*10^12 in Meters, and its not an option when converted to mm

Now how are you getting that?? That's nowhere near 60/(0.36*sigma*(2853)^4). You really need to show more of what you are doing before anyone can figure out what you are doing wrong.

hmm,..okay i love how as soon as i decide to show some work and show u what I am puttin in my calculator i get an answer that's actually a multiple choice answer. wth!? i got 44mm^2

teggenspiller said:
hmm,..okay i love how as soon as i decide to show some work and show u what I am puttin in my calculator i get an answer that's actually a multiple choice answer. wth!? i got 44mm^2

So do I.

no pun intended

teggenspiller said:

no pun intended

I'm not sure what that means but I'm guessing it's not "thanks for helping".

thanks a lot for you help. i suddenly understand.

really though, i do appreciate it

teggenspiller said:
really though, i do appreciate it

Very welcome.

## What is the surface area of the filament?

The surface area of a filament can vary depending on its shape and size. Generally, the surface area of a filament can be calculated by finding the area of each side and adding them together. For example, the surface area of a cylinder filament can be calculated by multiplying its height by its circumference and adding the area of the two circular ends.

## What is heat expansion?

Heat expansion is the phenomenon in which a material expands when heated and contracts when cooled. This is due to the increase or decrease in the kinetic energy of its particles, causing them to move further apart or closer together. The amount of expansion depends on the material's coefficient of thermal expansion.

## What is heat transfer?

Heat transfer is the movement of thermal energy from one object to another due to a difference in temperature. There are three main types of heat transfer: conduction, convection, and radiation. Conduction is the transfer of heat through direct contact, convection is the transfer of heat through the movement of fluids, and radiation is the transfer of heat through electromagnetic waves.

## How does heat expansion affect the surface area of a filament?

When a filament is heated, it expands in all directions, including its surface area. This is because the particles in the filament gain energy and move further apart, causing the material to expand. The amount of expansion in the surface area will depend on the material's coefficient of thermal expansion and the change in temperature.

## Can heat transfer affect the surface area of a filament?

Yes, heat transfer can affect the surface area of a filament. When a filament is heated, it may also experience heat transfer from its surroundings, causing it to expand. In addition, if the filament is in contact with another object, heat transfer through conduction can cause the surface area of the filament to increase. However, if the filament is in a vacuum, there will be no heat transfer and therefore no change in surface area due to heat expansion.

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