To address your question about mass defect and energy, let's break it down into two parts, focusing on the principles of mass-energy equivalence and the specific scenarios you've presented regarding the combustion of petrol.
Understanding Mass-Energy Equivalence
According to Einstein's famous equation, E=mc², energy (E) and mass (m) are interchangeable; they are different forms of the same thing. This means that when energy is released or absorbed, there can be a corresponding change in mass. However, the changes in mass are typically very small and often negligible in everyday chemical reactions.
Combustion of Petrol: Initial Mass Change
When 1 kg of petrol is burnt in a closed chamber, it undergoes a chemical reaction with oxygen to produce carbon dioxide and water, releasing energy in the form of heat. The energy released during this process is approximately 47 MJ/kg. To find out how much the mass changes, we can use the mass-energy equivalence principle.
- First, calculate the energy released: 47 MJ = 47 x 10^6 joules.
- Using E=mc², we can rearrange it to find the change in mass (Δm): Δm = E/c².
- The speed of light (c) is about 3 x 10^8 m/s. Thus, c² = (3 x 10^8)² = 9 x 10^16 m²/s².
- Now, substituting the values: Δm = (47 x 10^6) / (9 x 10^16) ≈ 5.22 x 10^-10 kg.
So, the final mass of the chamber after burning 1 kg of petrol would be approximately 1 kg - 5.22 x 10^-10 kg, which is practically unchanged for all practical purposes.
Insulated Chamber Scenario
Now, let’s consider the second part of your question, where the chamber is insulated, meaning that the heat produced during combustion remains within the chamber. In this case, the energy released as heat does not escape, and the system retains that energy internally.
Even though the energy is contained, the mass change due to the heat energy remains the same as calculated earlier. The energy stored as heat can also be converted back into mass using the same principle:
- Again, using E=mc², the energy remains 47 MJ.
- Thus, the mass change due to the heat energy in the insulated chamber would also be Δm = (47 x 10^6) / (9 x 10^16) ≈ 5.22 x 10^-10 kg.
In summary, whether the chamber is closed or insulated, the mass change due to the energy released from burning 1 kg of petrol is approximately 5.22 x 10^-10 kg. This change is minuscule and typically imperceptible in practical terms, but it beautifully illustrates the relationship between mass and energy as described by Einstein's theory.
