# Introduction to thermal equilibrium

General context and concept preparation
Have you ever had the problem of how much hot water to put in the bath tub and how much cold water to get the mixture right. In many houses the hot water tap may give out water that is 55 to 60 degrees Celsius. This is uncomfortably hot whereas the cold tap often gives out water that is 15 to 20 degrees Celsius, cool to drink but a shock to shower in. This is often a real problem when adjusting the shower tap. Also we sometimes mix liquids and even ice to get our drinks to a comfortable temperature. These lessons will help us explore the science of these phenomena.
Episodes Equal volumes of water mixing Two to one volumes of water mixing Zero Celsius liquid water and ice mixing
Concrete preparation Point out and discuss 4 variables. Stress + and - change in temperature The idea of lower temperature water having heat transferred to it from the higher temperature water The first mixtures with 0 Celsius water being added to the hotter water takes us back to confirm episode 1
Cognitive conflict Often "Why do we not go hot into cold?" What do you predict will happen if we mix the hotter into the colder? Some predictions show temperature conflated with heat. The time needed for the ice to melt and the continuing fall in temperatures should be emphasised.
Social construction Mediate whether a small error in temperature is significant or not. Stress on the extensive variables of volume and mass. Stress ratio thinking to compare changes in temperature. Often discussions about why the need for stirring. These can be mediated to stress dynamic and statistical e.g to increase the chances of the ice meeting the warmer water.
Metacognition Should we not also do 50 ml:50 ml, 200 ml:200 ml? Fair up and down as in Beam balance. What range of ratios should we extend to. How do the predictions
compare with predictions in lesson 30?
Monitoring how we would represent the temperature fall compared to ris.
Bridging Discussion about lessons 28 and 30 where we had equal balanced arrangements. Reminders about inverse proportionality Links to prior work on rates of dissolving and evaporation. Links to ideas of states of energy systems.
Piagetian levels 2A/2B 2B*/3A 2B*/3B
Schemata Proportionality, simple equilibrium Proportionality and inverse proportionality, ratio, equilibrium Proportionality and inverse proportionality, ratio, equilibrium, formal models