61 lines
3.0 KiB
Markdown
61 lines
3.0 KiB
Markdown
---
|
|
title: Thermodynamics, Scattered
|
|
date: 2024-11-10
|
|
---
|
|
|
|
# A Couple of Equations
|
|
|
|
When it comes to energy transfer and phase changes there are only two useful equations.
|
|
1. **Specific Heat Equation**: This equation is used to calculate the heat required to change the temperature of a substance without a phase change.
|
|
$$
|
|
\Delta \textbf{KE}=Q = mc\Delta T
|
|
$$
|
|
- $Q$ = heat energy added or removed (in joules, J)
|
|
- $m$ = mass of the substance (in kilograms, kg)
|
|
- $c$ = specific heat capacity of the substance (in J/kg°C)
|
|
- $\Delta T$ = change in temperature (in °C or K)
|
|
|
|
2. **Latent Heat (Potential Energy Buildup)**: This equation is used for phase changes, where energy changes the state of the substance (like melting or boiling) without changing its temperature.
|
|
$$
|
|
\Delta \textbf{PE} = Q = mL
|
|
$$
|
|
- \( Q \) = heat energy added or removed (in joules, J)
|
|
- \( m \) = mass of the substance (in kilograms, kg)
|
|
- \( L \) = latent heat of the substance (in J/kg), which could be the latent heat of fusion (for melting/freezing) or vaporization (for boiling/condensing)
|
|
|
|
These equations together describe the heat energy required for changing the temperature of a substance and for changing its phase.
|
|
|
|
**It is important to note the alternate arrangement of both:
|
|
$$
|
|
Q=nc_{\mathrm{mol}}\Delta T = \Delta \textbf{KE}
|
|
$$
|
|
or for the other Latent Heat equation:
|
|
$$
|
|
\Delta \textbf{PE} = Q = nL_{\mathrm{mol}}
|
|
$$
|
|
|
|
- $n$ is the number of moles
|
|
- the subscript `mol` notates the same variable, but in units *per* mole.
|
|
- ==You might see both==, at least they were both on the concept builders.
|
|
|
|
# Black-body radiation
|
|
|
|
All objects/bodies emit electromagnetic radiation over a range of wavelengths. Cooler objects emit less radiation than warmer bodies, simply because of having less energy. An increase in temperature directly correlates with a smaller wavelength ($\lambda$), and a higher frequency ($f$ or $v$).
|
|
|
|
Radiation being *incident* means that it strikes or falls upon a surface, object, or body. Radiation that is incident on an object is partially absorbed and partially reflected. **Thermodynamic Equilibrium** is a state in which a body emits radiation at the same rate that radiation hits it. Therefore, a good absorber of radiation is also a good emitter. A perfect absorber absorbs all E.M. radiation incident on it. Such an object is called a *black body*. This doesn't mean no energy is emitted, however. A black body remits the radiation it absorbs as a thermal radiation in a spectrum determined solely by its temperature.
|
|
|
|
The intensity of the remissions of a black body is given by a function defined so:
|
|
$$
|
|
I(\lambda,T)
|
|
$$
|
|
|
|
Where $I$ is the *power* intensity that is radiated per unit of wavelength $\lambda$, per unit area of the black body. By multiplying the differential of $\lambda$:
|
|
|
|
$$
|
|
I(\lambda, T)\mathrm{d}\lamdba
|
|
$$
|
|
|
|
Provides the power per unit area of the black body, from the interval $\[\lambda, \lambda + \mathrm{d}\lambda\]$, given that $\mathrm{d}\lambda$ is an infinitesimally small quantity.
|
|
|
|
|