Skip to main content
K12 LibreTexts

2.12: U2.Solving a Thermal Math Problem

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    U2.Solving a Thermal Math Problem

    Emily van Zee and Elizabeth Gire

    1. State the problem in words
    2. Make a sketch of the amounts to be mixed
    3. Review what you know about the physics of this phenomenon: the relevant central ideas
    4. Draw a graph representing the problem (use a ruler to make straight perpendicular axes, draw flat horizontal lines to represent temperatures that are not changing before the two substances are mixed and the shared equilibrium temperature after the mixing, draw the appropriately shaped graph for mixing more hot than cold or more cold than hot or equal amounts. Draw the graph to indicate whether the changes in temperature happen very quickly or are gradual processes.)
    5. Tell the ‘story’ of the graph with the relevant central ideas to explain why the equilibrium temperature is likely to be where you have drawn it (nearer the temperature of the initial hot water, initial cold water, or in the middle.)
    6. Represent this scenario mathematically: State the equationin words that relates the masses of the substances mixed and their changes in temperature. Use the experimental form of the equation derived from your exploration or the theoretical form based on the Conservation of Energy and justify the use of the equal sign accordingly.
    7. Define symbols, state equation in symbols, and express how you are envisioning this equation.
    8. Solve for the unknown in symbols
    9. Record given values and estimate any needed
    10. Substitute values and calculate answer
    11. Check answer: why does the number you get from the calculation seem reasonable?

    2.12: U2.Solving a Thermal Math Problem is shared under a CC BY-SA license and was authored, remixed, and/or curated by LibreTexts.