Mass and Energy

Would the mass of burnt firewood be equal to the mass of firewood before burning?

Then where does that heat come from?

According to Einstein's equation, $E=mc^2$ Shouldn't there be some mass going out of the Earth which contradicts the law of mass conservaton?

Answer

Would the mass of burnt firewood be equal to the mass of firewood before burning?

You won't get a good answer by simply looking at the "burnt firewood". The combustion is using oxygen from the air, and it is creating carbon dioxide and many volatilized materials that will disperse in the air. But we can imagine combustion happening in a box that is sealed to retain any materials (such as smoke and gases), but which allows energy (perhaps in the form of heat and light) to leave. If done to a very high precision, there would be a tiny difference found in the measured mass. The difference would be equal to the energy liberated during the combustion.

A generous value for the amount of energy liberated due to combustion would be $20MJ/kg$. If we were to combust a $1kg$ log in the presence of sufficient oxygen, then the mass deficit would be on the order of $$m = \frac{E}{c^2} $$ $$m = \frac{2\times 10^7 J}{9.0\times 10^{16}\frac{m^2}{s^2}}$$ $$m = 2.2\times10^{-10}kg$$ This difference in a $1kg$ mass is not measurable.

With such small differences, we can assume that mass is conserved during chemical reactions. When nuclear reactions are considered, the amount of mass converted becomes large enough to be measured and the law of mass conservation has to be modified.