Spontaneous Combustion My teacher posed this question in class and it stumped me, primarily based on my lack of fundamentals of thermodynamics:
Peter Griffin was sitting around when all of a sudden he spontaneously combusts (Based on an episode). Is this possible and if not, under what circumstances is this possible?
My reasoning is
$${\rm Peter + O_2 \to H_2O + CO_2 }$$
There are more gas particles so entropy must increase, $\Delta H$ is negative since it is a combustion reaction and so according to
$${\Delta G = \Delta H - T \Delta S}$$
Meaning free energy decreases... Which doesn't seem to make sense because it's highly unlikely that humans spontaneously combust. This got me thinking that the reaction itself is spontaneous. It just does not proceed because it cannot start the reaction due to insufficient activation energy (Particles not travelling fast enough).
My teacher said $\Delta H$ is positive which makes no sense to me... In a combustion reaction energy is released. He said it only occurs at very high temperatures because $T\Delta S$ is large enough to counter the positive $\Delta H$.
Is my teacher right or is my reasoning more correct?
 A: Most reactions have an activation energy. This means that although overall the reaction produces energy you initially have to put some energy in to get the reaction going.
Take for example the combustion of hydrogen in oxygen:
$$ 2\text{H}_2 + \text{O}_2 \to 2\text{H}_2\text{O} $$
This is an exothermic reaction and also has a positive entropy change, so you'd expect it to have a negative free energy change. And indeed it does. But you can mix hydrogen and oxygen at room temperature and they will not react. In order to make them react you need to add some energy, e.g. as a spark, and the reaction will then go with a bang!
The reason for this is that to make the molecules react they first have to split into their component atoms, and that takes a lot of energy. Once the reaction gets going the heat released is enough to provide this activation energy, but at room temperature the hydrogen and oxygen molecules simply do not have enough energy for their collisions to split them into separate atoms.
In the particular case of burning solids (like Peter!) there is another reason an activation energy is needed. As a general rule the activation energy needed to pull an atom out of a solid, so it can react with gaseous oxygen, is very high. Combustion is actually a gas phase reaction. When you burn, e.g. wood, the heat of the flame produces volatile gases from the wood. these gases burn and the resulting heat produces more gases, and so on. That's why to make wood burn you need to provide heat first.
Incidentally there's another reason Peter won't burn. He is full of water (unless you have mummified him first) and water absorbs heat by turning to steam. That means it tends to cool reactions and deprive them of the activation energy they need to keep going.
As it happens human bodies do burn, especially if they contain a lot of body fat, but it does take a source of heat to set them off. Typically heat melts the body fat, the fat wicks onto clothes and then vaporises and burns just as the wax does in a candle. The heat liberated is then enough to make the less volatile tissues burn as well.
A: Good Effort! 
We can make an analog case for "spontaneous". Assuming there is a hill, when you put a ball on top of the hill, it will spontaneously roll down the hill. On the contrary, if you put the ball at the foot of the hill, it will not spontaneously roll up the hill. Potential energy plays a role here.
For a chemical reaction, it is the same, if free Gibbs change between an initial state and a final state is negative, the mixture will spontaneously react changing from initial state (Peter + $O_2$) to the final state ($H_2O+CO_2$).
$\Delta H$ is another thing. If it is negative, as you can be sure, the free Gibbs energy is negative. So it is a spontaneous process. If it is positive, which is more useful in practical application, it can be spontaneous if it is less than $T \Delta S$. Otherwise it is not spontaneous.
A: There are several ideas here to separate out. 
First, can a body burn? Certainly large parts can; fat is flammable and Peter Griffin has some. 
But will it ignite?  Flammable materials have an “auto ignition” temperature at which they will ignite. Different materials do this at higher or lower temperature. When lighting something with a match, you heat a small part hot enough to ignite, that combustion heats more to a high enough temperature, and it proceeds. On the other hand, if something is cooling it, then enough new material might not reach the auto ignition temperature and the fire goes out. 
Finally, “spontaneous combustion” usually means a process where some slow oxidization reaction (i.e. in a hay bale or compost pile) generates heat which builds up, raising the temperature, which speeds the reaction, more heat, higher temp, faster reaction, until finally the auto ignition temp is reached and combustion starts. 
Could that happen in a person? Dunno. Some think so, some think the human body is really good at moving heat around to preserve homeostasis. 
