Chapter 2.

The situation refers to liquid water turning into steam. It is not usually useful to use “liquid water” as our physical system here because some of it “disappears”. On the other hand, what doesn’t disappear is are the water molecules so lets choose all of the water molecules as our physical system so that the system (some of them may make up the liquid and some make up the gas but the total number is constant). The interaction we are interested in is defined for us in the description of the situation. We start with purely liquid water at 100°C and end with purely gaseous water (steam) so those are our endpoints.

In the liquid state the H2O molecules are stuck to each other (they are bound to their neighbors by hydrogen bonds). But in gas state the molecules are separated apart so bonds must have been broken in the process of boiling. You have to add energy (bond energy) to break bonds so bond energy must have been added to the water to boil it (i.e. bond energy went up).

The situation explains that the initial temperature (T = 100° C) and the final temperature (T = 100° C) are the same. Since our model tells us that the indicator of thermal energy change is the temperature, the constant T tells us that the thermal energy did not change.

You should understand at least two ways of thinking about this situation. i) You have probably have common knowledge that you have to add heat to something (e.g. turn on the “burner” on the range) to boil it. That would tell you that the arrow points in. ii) Your physics knowledge tells you that the bond energy went up (bonds were broken) and that the thermal energy did not change (no temperature change). From this you can say that the total internal energy (Eth + Ebond) increased and, according to our energy-interaction model, the total energy of a physical system can only increase if energy was added to it so heat must have been added. To check that we are consistent, note that the “Heat” arrow points inward and Bond E goes up.

From previous questions, you have learned that the energy diagram looks something like the picture to the right. The only thing missing is the “conservation of energy” equation relating the energy changes with the energy transfers. The sum of the energy changes equals the energy transferred. ∆Eth +∆Eb=Q Note that ΔEth = 0 and ΔEbond > 0 so Q > 0 which tells us that heat was transferred in. In other words, the change (increase) in the bond energy is exactly equal to the heat added.

Molecules are disappearing and new molecules are appearing but the total number and types of atoms doesn’t change so a reasonable physical system could be “all the atoms involved in the interaction”. Note that sunlight is not “matter” and so is not a part of any physical system. For energy conservation situations you will usually choose a time before the relevant interactions as the starting time (i.e. before the sunlight hits the physical system) and an ending time after all the relevant interactions are done.

For the purposes of bond energy changes, we can pretend that the reaction proceeds by first breaking up the reactants into atoms and, after that, forming the products from the atoms. Let’s think about the reactants first. Breaking bonds (without forming any new bonds yet) always requires that energy be added so the bond energy of the reactant had to increase (to break them up into atoms). Hence the upward arrow. Now the products. Forming bonds always requires that energy be removed (forming bonds is the opposite of breaking them) so the bond energy of the products must decrease. Hence the downward arrow.

The story of this situation doesn’t tell us about temperature. However, thinking about the real situation should convince you that a leaf is not continually heating up and heating up as photosynthesis proceeds within it. Since our model tells us that the indicator of thermal energy change is the temperature, the constant T tells us that the thermal energy did not change (this is probably an approximation but it is very likely to be a good one). Hence, in the diagram to the right no change is shown.

Sunlight (energy) absorption makes this reaction possible so we conclude that energy is entering the energy system from the outside (from the sun) so we draw the arrow pointing inward.

a) From previous questions, you have learned that the energy diagram looks something like the picture to the right. The only thing missing is the “conservation of energy” equation relating the energy changes with the energy transfers. The sum of the energy changes equals the energy transferred. We leave Eth out because ΔEth = 0 and get: ∆E_"b reactants" +∆E_(b products)=Q Note that Q represents the sunlight energy that was transferred in (so Q > 0). b) Sunlight energy was added so Q > 0 so (∆E_"b reactants" +∆E_"b products" )>0 and we can conclude that the increase in the bond energy of the reactants is larger than the decrease in the bond energy of the products.