Time to heat/cool

You don't need to guess, but you do need more information than is supplied here. Since heat is electromagnetic energy, its rate of travel is at a maximum in a vacuum, and less traveling through other substances. The rate of heat transfer depends on the temperature differential of the objects involved, as well as their area of contact and their ability to conduct heat.

The simplest case simply assumes that those objects are in such intimate contact that the heat transfer is essentially instantaneous. In the real world it seldom is. Thermodynamics is a fascinating topic, and extremely useful, but the resources of this forum are for the most part not equal to offering a semester's knowledge in a paragraph or two.

The answer to your question involves the the term "thermal time constant". You can look it up in any text on heat transfer, or get a good feel for it from wikipedia, or Google. It's a little too involved to explain in detail here, but it's not a vey complicated concept.

If the text is not easy to read I am sorry but it is all i could do. If you want to have a better look then send your e-mail address and i shall send you it in .doc format. As one of the commentators wrote it is simple but you cannot find it every where. I hope it is clear but if you have still questions please ask. The assumption of "instantaneous" transfer is totally out of question since heat is traveling at a speed which depends on material properties and i dare say that assuming it with "light speed" is a very big error or at least a too simplistic simplification. To make it clear the above equations could be a good approximation for a piece of metal in water but are far from reality for a piece of stone in a heavy oil. Even in the case of metals there are big differences between difusibility values so that a cooper piece will be more homogen in temperature than a piece of stainless steel. For steels the best example of difusibility limitations is the quenching test "jominy". If the speed of heat transfer would be so big as assumed the hardness will not depend on the distance to the cooled surface since the temperature change would be every where the same. A simplified model has never the less be respectful of physics.

Heat transfer rates and equilbration times are the subject of kinetics rather than Thermodynamics. Factors such as surface areas available for transfer of heat are controlling rather than the basic masses of the materials involved in the transfer.

Search on google and get your units, juggle the equation to get what you need.

watts =

mass (kgs) x Specific Heat Capacity (K cal Kg deg C) x Temp difference

860 x Heat Up Time (hours)

NB dont forget that you must add in the primary or secondary item to be heated, eg. 600Kg of water and the 200grm pot to get a correct wattage.

Seems like these are exam/test questions...

What I am doing is going over some basic questions in preparing to study for the PE. I started thinking what basic assumptions are to made or formulas/theories to apply to get the times for the heating.

These aren't "involved" questions, as the temp answers are very easy, nor are they homework questions, just "would like to know if" questions. Practical/"simple" solutions are sought no second semester thermo or heat transfer course lecture is requested.

More on line of "on the back of a napkin" formulas.

Thanks for the help/guidance.

The formula should be the same on either side of the napkin. The most important thing to remember is that the temperature change with time will not be linear. It will be exponential and will involve the natural logarithm to the power of -t/rc where t is time, r is thermal resistance, and c is heat storage capacity. The product rc is called the thermal time constant. It is the same equation that applies in electrical engineering to the electrical current versus time when discharging a capacitor through a resistor. The equation is very common in almost all branches of engineering, and you should become familiar with it.

I would like to know if, when writing your comment, you had a look at#3

Answer #2 spoke of the term "thermal time constant". Answer #3 gave a more complete description but was not very legible on my monitor. Answer #7 described the basic math used to calculate thermal time constant. If one remembers nothing else, one should remember that after one time constant, (RC), the temperature, voltage, or whatever parameter you are dealing with, will have changed close to 63.2% of its steady state change.

the natural logarithm to the power of -t/rc

logarithm is the power of a base to obtain a value in the case you discuss the base "e" is at the power -t/rc i.e. the last is the logarithm and is not at a power.

as an example: log(1000)in the basis 10 is 3 because 1000 = 10^3