Boltzman Constant, Emissivity and Surface Area of a filament

In summary, the Boltzmann Constant (symbol: k) is a physical constant that relates the average kinetic energy of particles in a gas to the temperature of the gas. It is important in science because it helps us understand and predict the behavior of molecules and atoms in various states of matter, such as gases, liquids, and solids. Emissivity, defined as a measure of how well a surface emits thermal radiation compared to an ideal black body, plays a crucial role in the study of heat transfer in thermodynamics. It can change over time due to various factors and is an important consideration in experiments and equipment design. The surface area of a filament directly affects its emissivity, with larger surface areas emitting more thermal radiation. The Boltz
  • #1
kavamo
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Homework Statement



A tungsten filament in a lamp is heated to a temperature of 2.30 x 10^3 K by an electric current. The tungsten has an emissivity of 0.31. What is the surface area of the filament if the lamp delivers 35.0 W of power?

Homework Equations

Stefan's Law

(a greek letter that looks like P?) P(net)=ekAT^4

The Attempt at a Solution



35.0=0.31(5.670x10^-8 w/m^2*K^4)(2.30*10^3)^4A

35.0 = 491876.5257A

35.0/491876.5257=A

7.1156069x10^-5


is this correct?

Thanks in advance for your help.
 
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  • #2
Problem solved! Thank you.
 
  • #3


I would like to commend you on correctly using Stefan's Law to solve for the surface area of the tungsten filament. Your calculations appear to be correct, and your final answer of 7.1156069x10^-5 m^2 seems reasonable. However, I would recommend including units in your final answer to ensure clarity and accuracy. Overall, good job on this problem!
 

Related to Boltzman Constant, Emissivity and Surface Area of a filament

1. What is the Boltzmann Constant and why is it important in science?

The Boltzmann Constant (symbol: k) is a physical constant that relates the average kinetic energy of particles in a gas to the temperature of the gas. It is important in science because it helps us understand and predict the behavior of molecules and atoms in various states of matter, such as gases, liquids, and solids.

2. How is emissivity defined and what is its significance in thermodynamics?

Emissivity is a measure of how well a surface emits thermal radiation compared to an ideal black body at the same temperature. In thermodynamics, it plays a crucial role in the study of heat transfer, as it determines the amount of thermal radiation that a surface emits or absorbs.

3. Can the emissivity of a surface change over time?

Yes, the emissivity of a surface can change over time due to factors such as surface oxidation, changes in surface roughness, and temperature fluctuations. It is important to consider the emissivity of a surface when conducting experiments or designing equipment that involves heat transfer.

4. How does the surface area of a filament affect its emissivity?

The surface area of a filament is directly proportional to its emissivity. This means that the larger the surface area, the higher the emissivity and the more thermal radiation it will emit. This is why materials with high surface area-to-volume ratios, such as thin wires or foils, are often used in applications that require efficient heat transfer.

5. Can the Boltzmann Constant, emissivity, and surface area of a filament be used to calculate its temperature?

Yes, the Boltzmann Constant, emissivity, and surface area of a filament can be used in conjunction with other thermodynamic equations to calculate its temperature. However, other variables such as heat flux and material properties must also be taken into account for an accurate calculation.

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