Woke up, fell out of bed. Dragged a comb across my head.
Found my way downstairs and drank a cup.
And looking up, I noticed I was late.

("A Day in the Life," by the Beatles, 1967)

 

MORNING COFFEE

As the world turns so do the coffee grinders ...

while the French presses plunge downward ...

and the drip coffee makers percolate.

The universal ritual to start the day .... and continue the day ... and even end the day... is to make and drink a hot cup of coffee.

That anticipated first cup of Joe transforms the groggiest of beasts into a more civilized human being.

The groggy beast can't live without it ...

nor can the family that puts up with the groggy beast live without that morning cup of coffee.

The morning ritual continues as the liquified essence of  roasted ground coffee beans diffuses throughout the room: 

Let out the cat.

Grab the paper...or cell phone... or electronic pad of some type.

The cup of coffee is now at the perfect Goldilocks temperature... not too hot, not too cold...just right.

Time to sit down to savor that perfect cup of coffee wherever you are.

Even if on the rooftop of a house.

A passing thought: How did I get here? Whatever. The world will be alright again after you drink that cup of coffee cradled in your hand.

But some days there is disturbance in the cosmos.

That cell phone rings.

The baby needs changing NOW.

Sounds like that cat you put outside is being mauled by the pit bull that moved in with the new family down the block.

By the time you return to your cup of coffee you know by repeated experience that it no longer is at the perfect Goldilocks temperature.

No longer do coffee vapors billow up from the liquid's surface.

Alas, no joy.

The coffee is now at the same ambient temperature of wherever you left it.

You instinctively knew by experience that would happen.

But why did the heat transfer out of the coffee and where did that anticipated warm glow of heat go?

And why is the coffee at the same temperature of wherever you left it before changing that diaper or rescuing that darn cat?

 

ATTRIBUTES OF THIS THING
THAT WE ALL CALL  "HEAT"

1. Heat is flowing thermal energy.

Heat is always in transit, always moving. When the moving stops...there is no longer "heat."

Ergo, there is no such thing as stagnating heat.

Heat may be "stifling" but it is never stagnant.

 

2a. Heat is totally dependent upon not one but two temperatures to exist.

Furthermore,

2b. One of the temperatures must be hotter than the other temperature.

3. Definition of Temperature Differential.

The difference between the two temperatures is called the "Temperature Differential."

The  Temperature Differential is calculated by subtracting the cold temperature from the hot temperature:

Temperature Differential =

Hot Temp (°F or °C)  -  Cold Temp (°F or °C)

Temperature Differential is also called "Delta T."

Temperature Differential is also written in shorthand  "ΔT"; the triangle is the Greek letter "delta" and fancy educators of yore decided that it means "difference between" in written expressions.

Yes, indeedo!  Scribbling down a little triangle is a lot easier than writing "the difference between."

 

4. Equality Rules! The Universe does not tolerate Temperature Differentials.

Once a Temperature Differential (aka Delta T and ΔT) exists, Heat must move to equalize the temperature between the hot and cold regions until the difference in temperatures is gone.

The above graph shows what happens in a shared environment that has an area at 70 °C ( 158 °F) and and area at 5 °C ( 41°F).

Over a few minutes, heat is transferred until a common temperature of 30°C (86°F) is the ambient temperature of the shared environment.

Heat cannot help but move to equalize temperatures; the universe must want everything to be happy at the same temperature!

Equal final temperature for all!

 

5. Heat MUST Transfer from the HOT to the COLD temperature. 

Heat is always transferred out of the hotter area and into the colder area, never ever in the other direction.

As stated above, the transfer of Heat continues until the two temperatures are at the same final temperature,

When temperature equilibrium is achieved, the Temperature Differential no longer exists.

Then the heat transfer is over.

Which means this concept we all know as Heat no longer exists....

because heat is "flowing thermal energy."

And without a Temperature Differential there is not driving force for heat to flow.

And all that remains is matter that is at the same temperature.

Prove it to yourself:

Touch all the non-living surfaces in the middle of the room that you are in and you will feel that they are all at the same temperature. Just don't be near the windows or a heater.

 

 6. The greater the Temperature Differential, the greater the rate of heat transfer. 

The Temperature Differential (aka Delta T and  ΔT) is the driving force for heat transfer.

The greater the Temperature Differential (aka Delta T and ΔT), the more heat is transferred in a time interval.

 

SO WHY DID THAT CUP OF COFFEE
COOL DOWN TO ROOM TEMP?

The temperature of a perfectly brewed cup of coffee is 200 °F/ 93 °C  (however, fast food giant McDonald's learned in a law suit that the coffee should be served at no greater than 175 °F/ 79 °C).

On the other hand,  'tepid' cup of coffee is in the 130°F/ 54 °C  to 150°F/ 66 °C range.

Pretend that there is a thermometer in an insulated cup of brewed coffee.

And assume the room temperature is 65°F (20 °C).

Below is a graph that shows the temperature of the   coffee decreasing as it sits unattended for 200-plus minutes (3.33 hours and then some).

At the very beginning, the Temperature Differential between the 200 °F hot coffee and the 65°F room is at  its greatest magnitude of 135°F:

Hot Temp (°F or °C)  -  Cold Temp (°F or °C)

(200°F - 65°F) = 135°F

 

PTOA Readers and Students should notice how the graphed line shows that the temperature of the coffee plunges downward before it gradually levels out at the room temperature (65°F, unfortunately not written on the Y-axis).

The plunging part of the line illustrates that the sensed temperature of the coffee rapidly decreases as it transfers its heat into the surrounding colder ambient environment.

As the graph shows, the rate of heat transfer is greatest at the beginning because the Temperature Differential is the greatest between the hot coffee and colder ambient temperature.

Within the first 20-30 minutes the coffee has transferred heat into the surrounding atmosphere and is at the 'tepid' temperature range; the coffee is no longer "hot" but "warm" and the rate of heat transfer likewise decreases.

The Temperature Differential between the coffee and room decreases until the coffee has transferred all its heat and is at 65°F, the same temperature of the room.

Once the coffee is 65°F, Temperature Differential is zero.

The driving force for transferring heat is gone.

Heat no longer exists!

Why? Because heat is defined as constantly flowing energy... and the flowing has ceased.

 

HEAT SINKS

Why didn't the temperature of the room change?

After all, in the graphic to the right, a shared area of hot and cold temperatures eventually line out to a  new temperature balanced between the two.

The graphic to the above right shows what happens when the hot and cold areas are more equivalent in magnitude.

A small cup of coffee situated in a typically sized room is a different matter altogether.

The amount of air surrounding the coffee cup is too vast of a Heat Sink to detect any difference in the ambient temperature of the room.

A Heat Sink exists when the final sensed temperature of the cool area is not changed after the heat transfer has been completed.

The heat was transferred from the coffee, but the amount of heat was too small to cause a change in the air temperature.

Otherwise stated:

The total content of thermal energy in the small cup of coffee was not a sufficiently large quantity to make a change in the ambient temperature of an entire room even after the transfer of heat had been completed.

A bigger cup of coffee would have made more of an impact on equalizing the ambient temperature of a small room.

 

TAKE HOME MESSAGES: This PTOA Segment introduced Heat.

The driving force that creates heat is a Temperature Differential caused by a hot and a cold temperature.

Additional expressions for Temperature Differential are "Delta T" and  "ΔT."

The greater the Delta T, the greater the rate of heat transfer.

The Delta T constantly decreases during the process of exchanging heat because the two temperatures are getting closer and closer toward an equilibrium temperature.

Heat always flows... is transferred from... the hot area into the cold area.

Heat transfer continues until the previously hot and cold areas are at the same temperature, which can be a temperature between the hot and cold temperatures that existed before heat transfer began.

Heat Sinks exist when the cold temperature remains at the same temperature even after the heat transfer has been completed.

©2015 PTOA Segment 00058
PTOA Heat Transfer Focus Study Area

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