Does the weight of the exhaust weigh the same as the weight of the gas?

Question

I once read that the weight of the planet has not changed in millions of years (only increased due to celestial objects that have collided with our planet). This fact has always confused me as it pertains to the consumption of energy.

For example, if you burn a log, does the combination of the ash weight and the smoke weight equal the weight of the log?

The same question could be applied to consumption of food and burning gas and coal. Does anybody know the answer to this?

Answer 1

Yeah it does.  Conservation of mass states that you can't destroy matter. When you burn a log, the sum of the ashes and exhaust gas equals the mass of the log.

Answer 2

Our planet earth always increases in mass as space dust, asteroids etc constantly falls on it. Remember the law of conservation of energy " Energy can neither be created nor be destroyed. It can only be transformed from one form to another in an equivalent amount".

To give you a simple explanation let us consider Einstein's mass energy relation. E=m*C^2. According to this equation mass and energy are like two sides of a coin. If you burn something completely you will get its mass equivalent of energy.

But in practice combustion is always incomplete which means not all the matter gets converted to energy. okay.

If you burn a log you will get heat, ash and smoke. The sum of all should be equal to the mass of the log. For example let us consider a wooden piece with 15% water content. It has a calorific value of 16 MJ/Kg. It is the amount of heat you would get if you burn 1 Kg of wood.

Substituting this mass value in Einstein's mass energy equation as follows,

E=M*C^2.

   = 1*(3*10^8)^2 = 9*10^16. ( pretty huge value!!!)

The energy that you should get is 9*10^16 joule. This is the energy equivalent of wood of one kilogram.

compare this to the calorific value of 1 kg of wood which is 16*10^6 joule which is the actual value that you get by burning one kilogram of wood.

dividing one by the other (16*10^6)/(9*10^16) = 1.777*10^ -10

Which means only 1.77*10^ -10 of the part of wood is converted to energy which is a negligible amount.

Therefore, the sum of ash and smoke will be equal to its initial weight. Since only a fractional part of is converted into energy

the mass that is converted into energy is negligible . Only in energy conversion like nuclear reactions will the mass change be appreciable. That is if you add the end products it will not be equal to the initial mass as a larger amount of mass is converted to energy unlike burning a log. The mass that is converted into energy in a nuclear reaction is also a tiny fractional part of the original mass but higher than burning a piece of log.

conclusion:

      If you find all the mathematical part hard to understand, bear this in mind. By burning a piece of log you get energy that is heat. If you add the smoke and ash it will be equal to its  original mass. only a very tiny percentage of the mass is lost to give heat. That mass can be ignorned in practice.