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https://notendur.hi.is/hj/EE2/HD1lausn.pdf
Eq. \ref{eq:5888046} is an initial equation. \begin{equation} \alpha = \frac{1}{V} \left( \frac{\partial V}{\partial T} \right)_p \label{eq:5888046} \end{equation} Eq. \ref{eq:5927974} is an initial equation. \begin{equation} V = \frac{n R T}{P} \label{eq:5927974} \end{equation} Substitute LHS of Eq. \ref{eq:5927974} into Eq. \ref{eq:5888046}; yields Eq. \ref{eq:7236464}. \begin{equation} \alpha = \frac{1}{V} \frac{nR}{P} \left( \frac{\partial T}{\partial T} \right)_P \label{eq:7236464} \end{equation} Simplify Eq. \ref{eq:7236464}; yields Eq. \ref{eq:4600503}. \begin{equation} \alpha = \frac{nR}{VP} \label{eq:4600503} \end{equation} Eq. \ref{eq:5130250} is an initial equation. \begin{equation} P V = n R T \label{eq:5130250} \end{equation} Divide both sides of Eq. \ref{eq:5130250} by \(T\); yields Eq. \ref{eq:8283443}. \begin{equation} \frac{PV}{T} = nR \label{eq:8283443} \end{equation} Substitute RHS of Eq. \ref{eq:8283443} into Eq. \ref{eq:4600503}; yields Eq. \ref{eq:7845152}. \begin{equation} \alpha = \frac{PV}{T} \frac{1}{VP} \label{eq:7845152} \end{equation} Simplify Eq. \ref{eq:7845152}; yields Eq. \ref{eq:2491768}. \begin{equation} \alpha = \frac{1}{T} \label{eq:2491768} \end{equation} Eq. \ref{eq:2491768} is one of the final equations.