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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.

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

trula
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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.......

Spandan Kundu
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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 $E=mc^2$

Nakshatra Gangopadhay
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  • Thank you very much for explaining me. But as you said burning hydrogen doesn't convert all its masses into energy, but I think I can calculate the percentage of hydrogen getting converted into energy. Can I? – Scarlett Aug 20 '21 at 17:56
  • @Scarlett think of it in this way. When you burn wood, all the molecules of hydrogen get converted into soot, dust, smoke, etc. But if you could theoretically find each and every one of these molecules, and measure the total mass, you'll find that it is the same. This is because combustion is a chemical reaction, mass is conserved. So, mass is not converted into energy here. – Nakshatra Gangopadhay Aug 20 '21 at 18:11
  • @Scarlett the only way mass is converted into energy is when it is destroyed or annhilated. This happens in a nuclear reaction. In those reactions, if you weigh the mass before and after, they won't be the same. This difference in mass gives rise to energy. This destruction of mass serves as the source of energy. – Nakshatra Gangopadhay Aug 20 '21 at 18:13
  • @Scarlett but in combustion, mass is not destroyed or created. Yeah, the mass of hydrogen decreases, as it is converted into something else, water for example, but it is not 'destroyed' like in a nuclear reaction. The source of the energy is from the bonds that hold the molecule together, reacting with oxygen. – Nakshatra Gangopadhay Aug 20 '21 at 18:14
  • @Scarlett from the formula I've given $Q=mc\delta T$, if you know the total heat, temperature difference, and specific heat capacity, then you can find mass $m$. If you had a total mass $M$, then you could find the percentage of mass burnt by $\frac{m}{M} *100$. Remember, burnt and destroyed is different. Hope this helps. – Nakshatra Gangopadhay Aug 20 '21 at 18:17
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    @NakshatraGangopadhay, mass is "lost" in burning, it is just that the amount lost is so small you cannot easily detect it. Nuclear reactions aren't different in character from chemical reactions, they just release more energy so the mass deficit can be measured more easily. – BowlOfRed Aug 20 '21 at 18:41
  • @BowlOfRed yeah agreed, there is some loss of mass, in chemical reactions, but primarily the energy comes from the enthalpy of combustion. The energy due to loss of mass, is negligible compared to this, in chemical reactions, and we normally assume conservation of mass. – Nakshatra Gangopadhay Aug 20 '21 at 18:47
  • Yes, the mass loss is so small that conservation of mass is fine to assume. But to say that the energy comes from one place instead of another is incorrect. The enthalpy of combustion is exactly the same as the energy due to mass loss. – BowlOfRed Aug 20 '21 at 18:50