How do we calculate the amount of mass converted into pure energy when we burn 1 kg of hydrogen?

Question

I wanted to know how much mass and the percent of hydrogen converted into pure energy when $1\,\text{kg}$ of hydrogen is burnt. Let's suppose $1\,\text{kg}$ of hydrogen burns into $12\cdot10^7\,\text J$. I was thinking of solving it using $E=mc^2$, do you think it is possible? I am new in physics, so please go easy on me.

Answer 1

$E/c^2$ gives the right answer for the combined loss of mass of the $H_2 and O_2$ molecules

Answer 2

When hydorgen is burnt in air, it simply react with the oxygen present in the air and produces water and releases few energy. If you add the mass of hydrogen and oxygen and subtract the mass of water formed from the combined mass, you will get a very very small difference (practically you will get no difference) that difference is the mass converted into energy. Another way you have said that if you can measure the energy released, you can divide it by c² , you can all find it( m= E/c²). But there is a problem. Note that in case of burning the mass coverted into energy is extremely small (near to zero) as it is chemical reaction. So the better way to test the application of Einstein's mass energy equivalence is nuclear reaction of radioactive elements( because the elements are Highly unstable) like nuclear fission and fusion where the loss of mass is measurable so as the energy.

Hope it helps.......

Answer 3

The keyword here is burning of hydrogen. The mass-energy equivalence relation that you stated above $E=mc^2$, is used when mass is converted completely into energy. This is only possible in nuclear reactions, or when you annihilate matter, using anti-matter. Simply burning hydrogen, doesn't convert all its mass into energy.

Take the example of a piece of wood. When you burn it, it doesn't get annihilated or destroyed. It gets converted into soot, ash, and a few other compounds, but what is really happening is that the different bonds inside the molecules break, and energy is released, as the compound combusts i.e. chemically reacts with oxygen.

You can calculate the amount of energy released using the calorimetry formula :

$Q= mc\delta T$, where $m$ is the mass, $c$ is specific heat and $\delta T$ is the change in temperature.

Another alternative way is to use Hess law from chemistry.

The energy is called the heat of combustion or enthalpy of reaction. It is different from $E=mc^2$