Electronics: Heat, Power, Conduction, and Resistance

 

The generalized Power law presents the equation to compute the amount of power that is used by a device as the following: 

P = VI

It says how much power is pumped into a circuit. We can use this to find the ammount of power pumped into the black box. 

Knowing how much power is pumped into a black box allows for quick consumption measurements and simplifies circuit analysis. Power can be converted into other weird forms that are not exactly heat. We can only say that power is converted 100% to heat energy is when our black box is a perfect resistor, or 100% Ohmic in nature. The generalized power equation is denoted by V^2 / R or I^2 R. The resistance can also be measured by P/(I^2). Here's an example of power loss in circuits: 

Now, we want to discuss thermal conduction and thermal resistance. Hotter molecules in a substance impart their energy to much slower moving particles. Heat transfer is the transfer of energy due to lattice vibrations, and the transfer can be enhanced by propagating lattice waves. Here, they propagate as phonons.

In metals, heat is the both the lattice vibrations as well as the kinetic energy transfer of electrons. Free electrons in a metal is moving fast. An increase in the metal temperature will decrease the drift velocity due to increased lattice vibrations and increased thermal energy component. However, the increase in temperature will also increase the resistance of the electrons. 

The change in internal energy is the addition of the Heat QH added to the system or the work W done to the system, or ΔU = QH - W. Here's the equation in how we transfer heat from on material to another:

Pheat = dQH/dt = -k∇T

Here is the gradient to express temperature differentials in 3D, and the power gradiant as a functio of the area A and Length L as well as the change in temperature ΔT:

Thermal resistivity is how bad a substance is at transferring heat. R is the thermal resistance is L/(kA) or λL/A. The power transfer of the heat accross the block of material is the following:

Pheat = dQheat/dt = k(A/L)ΔT = 1/λ (A/L) ΔT = ΔT/Rthem 

k = thermal conductance   λ = resistivity or Rtherm is thermal resistance. 

Thermal and electrical stuff have different properties, such as conductivity, resistivity, resistance current, potential difference, source. 

Here is the thermal resistance of copper wire: 

Every circuit component has internal resistances. Sometimes, though, temperature increases to critical point.

Use components handle 2-3x maximum dissipation, and this helps to lower the temperature coefficient. The methods to remove heat are heat sinks which increases the radiating surface in the air, layout, and ventilation. 

Now we want the calculate the the temperature change of the new resistor with the following measurements. The silicon layer, which is the semiconductor in the middle, is 0.002".