Exam.heat_of_vaporization

% ======== Initial values that may be altered ======
\newcommand{\substance}{gøysteinium\xspace}
\setfpvar{stepsTemp}{8} % Number of steps on the y axis
\setfpvar{maxTemp}{21*\fv{stepsTemp}} % Max temperature
\setfpvar{stepsTime}{8} % Number of steps on the x axis
\setfpvar{maxTime}{8} % Max time
\setfpvar{substanceAmountKg}{2*\randomint{2}{5}-1}
\setfpvar{power}{123*\randomint{1}{5}}
%
% ======== Now we do the temperature calculations ======
\setfpvar{scaleTemp}{\fv{maxTemp}/\fv{stepsTemp}}
\setfpvar{secondTemp}{1*\fv{scaleTemp}}
%
% The following lines finds the values for temperature randomization
\setfpvar{lowrangeTempL}{round(\fv{stepsTemp}*0.2)}
\setfpvar{highrangeTempH}{round(\fv{stepsTemp}*0.8)}
\setfpvar{lowrangeTempH}{\fv{lowrangeTempL}+1}
\setfpvar{highrangeTempL}{\fv{highrangeTempH}-1}
\fpcompare{\fv{lowrangeTempL}>1}{ }{
	\setfpvar{lowrangeTempL}{0}
	\setfpvar{highrangeTempH}{\fv{stepsTemp}}
}
% Randomizes the melting point and vaporation point
\setfpvar{constVC}{\randomint{\fv{highrangeTempH}}{\fv{stepsTemp}}}
\setfpvar{constFC}{\randomint{\fv{lowrangeTempH}}{\fv{highrangeTempL}}}
\setfpvar{constIT}{\randomint{0}{\fv{lowrangeTempL}}}
%
\setfpvar{heat_of_vaporization_C}{\fv{scaleTemp}*\fv{constVC}} % Scales up the melting point to match initial values
\setfpvar{heat_of_fusion_C}{\fv{scaleTemp}*\fv{constFC}}
\setfpvar{initial_temp}{\fv{scaleTemp}*\fv{constIT}}
%
% ======== Now we do the time calculations ======
\setfpvar{maxTimeSec}{60*\fv{maxTime}}
\setfpvar{scaleTime}{\fv{maxTime}/\fv{stepsTime}}
\setfpvar{secondTime}{1*\fv{scaleTime}}
%
% The following lines find the indicies for time randomization
\setfpvar{lowrangeTimeL}{round(\fv{stepsTime}*0.2)}
\setfpvar{highrangeTimeH}{round(\fv{stepsTime}*0.8)}
\setfpvar{lowrangeTimeH}{\fv{lowrangeTimeL}+1}
\setfpvar{highrangeTimeL}{\fv{highrangeTimeH}-1}
\fpcompare{\fv{lowrangeTimeL}>1}{ }{
	\setfpvar{lowrangeTimeL}{0}
	\setfpvar{highrangeTimeH}{\fv{stepsTime}}
}
\setfpvar{heat_of_vaporization_t}{\fv{maxTime}} % Uncomment the line below to vary heat of vaporization time
\setfpvar{time_2_vaporization}{\randomint{\fv{highrangeTimeL}}{\fv{maxTime}-1}}
\setfpvar{time_2_vaporization_sec}{60*\fv{time_2_vaporization}}
\setfpvar{heat_of_fusion_t}{\randomint{1}{\fv{lowrangeTimeL}}}
\setfpvar{heat_of_fusion_sec}{60*\fv{heat_of_fusion_t}}

\begin{problem}{\mylist{5, 5}}
	Grafen viser hvordan temperaturen forandrer seg i
	$\unitfv[3]{substanceAmountKg}{\kg}$ av stoffet \substance når det varmes opp
	fra fast form. Effekten som tilføres er \SI{\fv{power}}{\W}.

\begin{minipage}[t]{0.35\textwidth}
	\begin{subproblem}
		\label{subproblem:goysteiniumA}
		Hvor mye energi skal til for å smelte $\unitfv{substanceAmountKg}{\kg}$ \substance?
	\end{subproblem}
	%
	\begin{subproblem}
		\label{subproblem:goysteiniumB}
		Hva er den spesifikke smeltevarmen for \substance?
	\end{subproblem}
\end{minipage}
%
\begin{minipage}[t]{0.65\textwidth}
	\vspace{0pt}
	\begin{center}
    \begin{tikzpicture}
      \begin{axis}[
				grid=major,
				grid style={dashed,gray!30},
				axis lines=middle,
				enlargelimits=false,
				inner axis line style={-stealth},
        % unit vector ratio*=1 1 1,
        % axis line~style={draw=none},
        % tick style={draw=none}, % Remove axis line just for this plot
        width=0.75\textwidth,
				ytick={0,\fv{secondTemp},...,\fv{maxTemp}},
				xtick={0,\fv{secondTime},...,\fv{maxTime}},
				ylabel={\si{\celsius}},
				xlabel={t/\si{min}},
				ymin=-0.8,ymax=\fv{maxTemp},
				xmin=-0.8,xmax=\fv{maxTime},
        % xticklabel style={anchor=north~east},
        ]
				\addplot[ultra thick, UiT-blue] coordinates { (0,\fv{initial_temp})
					                     (\fv{heat_of_fusion_t},      \fv{heat_of_fusion_C})
				                       (\fv{heat_of_fusion_t},      \fv{heat_of_fusion_C})
														   (\fv{time_2_vaporization},   \fv{heat_of_fusion_C})
				                       (\fv{time_2_vaporization},   \fv{heat_of_fusion_C})
														   (\fv{heat_of_vaporization_t},\fv{heat_of_vaporization_C}) };
      \end{axis}
    \end{tikzpicture}
	\end{center}
\end{minipage}
\end{problem}

\begin{answer}
\setfpvar{energy}{
	\fv{power}*\fv{heat_of_fusion_t}*60/1000
}
\setfpvar{enthalpyOfVaporization}{
	\fv{energy}/\fv{substanceAmountKg}
}

\emph{\Cref{subproblem:goysteiniumA}} Effekten $P$ er energi (eller arbeid) per tid.
%
\begin{equation*}
	P = \frac{E}{t}
\end{equation*}
%
Den tilførte energien er altså
%
\begin{equation*}
	E = Pt
	= \SI{\fv{power}}{\W} \cdot \unitfv{heat_of_fusion_t}{min}
	= \SI{\fv{power}}{\W} \cdot \unitfv{heat_of_fusion_sec}{\s}
	% \approx
	\approxfrac[3]{\fv{power}*\fv{heat_of_fusion_t}*60}{1000}
	\unitfv[3]{energy}{\kilo\joule}
\end{equation*}
%
\emph{\Cref{subproblem:goysteiniumB}}
Smeltevarmen er varmen $Q$ som trengs for å smelte \SI{1}{\kg}
%
\begin{align}
	l_s = \frac{E}{m}
	\approxfrac[5]{\fv{power}*\fv{heat_of_fusion_t}*60}{1000}
	\frac{\unitfv[5]{energy}{\kilo\joule}}{\SI{\fv{substanceAmountKg}}{\kg}}
	\approxfrac[3]{\fv{energy}}{\fv{substanceAmountKg}}
	\unitfv[3]{enthalpyOfVaporization}{\kilo\joule\per\kg}
\end{align}
%
Den spesifikke smeltevarmen for \substance blir omtrent
\unitfv[3]{enthalpyOfVaporization}{\kilo\joule\per\kg}
som var det som skulle vises.
\end{answer}