“The body started at 273K in both cases.”

This is key. Why wasn’t the radiation absorbed from the colder body fully thermalised initially?

In the case of a common starting temperature, of course, the “parallel” lines in chart 3 are really divergent and dT/ds, the instantaneous measure of rate of change, for the pink one would be less than for the blue, in agreement with your average measure. This implies that the hypothesised radiation absorption or its thermalisation takes place gradually over time, which is at odds with other charts which show it occurring initially. Could it be that the second chart in Example 2 is, perhaps, a bit misleading?

]]>No and yes to the two parts of your first question. Yes, the graph displays two parallel lines separated by a constant temperature difference. (The lines, derived from chart 2, are curvilinear but appear linear over such a short time interval). No, the rate of temperature change, dT/ds, is the slope of the line, which is the same for both; Body 2 has no effect on Body 1′s cooling rate.

The body started at 273K in both cases.

– At 1000s the temperature reached about 155.5 when the body was on its own.

– At 1000s the temperature was almost 157 when the body was in the presence of the second (colder) body.

Rate of temperature loss in the first case (alone) = (273-155.5)/1000 = 0.118K/s

Rate of temperature loss in the seoncd case = (273-157)/1000 = 0.116K/s

They are clearly different.

Body 2 does have an effect on Body 1’s cooling rate otherwise both lines would be at the same temperature at the same time.

It’s pretty simple. Take another look.

]]>John, have you considered that, in example 2, one of the bodies has an internal energy source which is assumed to always keep it at the same “base” temperature?

Would it help to write down step-by-step what exactly happens at each time-step?

D.

]]>No and yes to the two parts of your first question. Yes, the graph displays two parallel lines separated by a constant temperature difference. (The lines, derived from chart 2, are curvilinear but appear linear over such a short time interval). No, the rate of temperature change, dT/ds, is the slope of the line, which is the same for both; Body 2 has no effect on Body 1’s cooling rate.

Do I think the graph portrays reality – your second question? No, for this reason: Consider the system comprising your two bodies. In an initial state, they are located beyond each other’s radiative influence and the system’s energy level is related to their temperatures. In a different state, the two bodies are within each other’s radiative influence and, you say, each raises the temperature of the other, thus increasing the system’s energy level. That is, energy has been created, a violation of the 1st law. In reality, energy would flow from the warmer region/body of the system to the cooler one thus conserving energy in accord with the 1st law, leaving the system’s energy level unchanged.

The source of the problem lies in your Note 2: Temperature change = net energy change / heat capacity.

You require a positive temperature change for each body which, given no change in heat capacity, mandates energy creation.

]]>My apologies, I missed the last line where you calculate the temperature.

D.

]]>..Visual inspection can be very deceptive and I would have liked SoD to include his actual formulas used to create the graphs.

The formulae are in note 2. I just used Excel and calculated the temperature and energy at each time step.

This is why it’s so simple – energy is conserved.

]]>