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content/physics/thermodynamics.md

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+---
+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.
+