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Could Some Tell Me Whether I'm Doing This Heat Energy Chemistry Problem Right Or Not?

Your work and answer is correct. You would only use the heat of steam value if the temperature went above 100C

1. Is radiation how heat energy travels in ...?

All of the above. In Vacuums heat transfer only occurs through radiation. In Gases or Liquids heat can be transferred via radiation, convection, or conduction.

2. What is the difference between thermal energy and electricity?

No idea what you mean by "this building has thermal energy". Eectricity is one of the highest grades of energy, 'lowest entropy' so it can be converted to other forms with high efficiency, like 99% to mechanical energy, or 100% to heat energy. Thermal energy is energy due to an objects temperature, the higher the temperature the lower its entropy [low entropy = more useful] The lower the temperature of something the less use the energy is. Eg, the air has thermal energy, but you can not do anything with that energy. For thermal energy to be of any use it has to be able to flow and for that there needs to be a temperature difference. Heat energy always flows from high temperatures to low. If we allow heat energy to flow through an appropriate machine we can extract some of the energy as mechanical or electric energy. The greater the temperature difference the greater the % of heat energy that can be converted. In a power station for instance a temperature difference of maybe 700C between the superheated steam and the exhaust steam allows for as much as 50% of the energy to converted to mechanical energy. In a system with just 50 C difference the maximum % that can ever be converted is very low. less than 8% [sorry forgot the exact equation] The flip side of this is that it is foolish and wasteful to use high quality energy and convert it to low quality energy like room heat. Eg an electric strip heater. That is like using gold foil to wrap your food in when aluminium foil will do just fine. [A better way to use electricity to heat a room is to use it in a heat pump, to pump heat from a lower temperature to a higher one. An efficient heat pump can deliver 5 times the energy you put in, eg a 500W heat pump can provide 2500W of heating, a 500W strip heater just 500W] Guess the real difficulty in understanding is that there really is no energy shortage at all, it is the entropy that is the issue. ie the quality of the energy! We are surrounded by lots of energy, because all objects around us are full of thermal and chemical energy, but that is energy we can not use because its entropy is too high. ALL things tend to greater entropy. You can think of entropy as the randomness of a system, the more mixed up and random, the higher the entropy and the less useful it is. eg. We find metal's in nature all mixed up in ores, we use high quality energy to separate them so we can use them. They we mix them up again and dump them in a landfill....

3. All energies change into heat energy at the end?

Much of it eventually gets radiated into space

4. A climate skeptic thinks "heat energy" is the same as electromagnetic radiation, how wrong is he?

The short answer is that it is much more complicated than people would like to admit. Heat is simply energy transferred from one body to another. An addition of heat energy to a system does not imply a temperature increase - an example is adding heat to ice and changing its phase from solid to liquid. This process requires energy but there does not have to be a temperature increase. In fact, it's possible for water to exist as solid, liquid and gas at a single temperature. Heat can be transferred in lots of ways. It can be transferred in the form of electromagnetic radiation. It can be transferred as vibrational energy in the form of phonons. And so on ... Thermodynamics is a statistical theory. It involves statistically examining the state of large groups of atoms or molecules. This is why the exact nature of heat is largely irrelevant for these calculations. So, if you want a precise definition of 'what is heat?' well, the short answer is that heat is simply a quantity of energy. What form that energy takes can be different, which is why we call it heat. Ultimately it must come down to interactions between particles. So, on a fundamental level, it must involve bosons like photons. But that's not the level we apply the concept of 'heat' to.

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