A fuel has mass densityρ and energy density u . What mass of the fuel has to be burned torelease thermal energy E

To find the mass of the fuel that needs to be burned to release a specific amount of thermal energy, you can use the following steps:

1. Understand the given quantities: The mass density (ρ) is the mass of the fuel per unit volume. The energy density (u) is the energy per unit volume. The thermal energy (E) is the total energy that needs to be released.

2. Use the definition of energy density: Energy density (u) is defined as the energy (E) per unit volume (V). So, we can write this as u = E/V.

3. Rearrange the equation to solve for volume: From the equation in step 2, we can solve for volume (V) by dividing both sides by energy density (u). This gives us V = E/u.

4. Use the definition of mass density: Mass density (ρ) is defined as the mass (m) per unit volume (V). So, we can write this as ρ = m/V.

5. Rearrange the equation to solve for mass: From the equation in step 4, we can solve for mass (m) by multiplying both sides by volume (V). This gives us m = ρV.

6. Substitute the volume from step 3 into the equation from step 5: This gives us m = ρ(E/u).

So, the mass of the fuel that needs to be burned to release a specific amount of thermal energy is given by the equation m = ρ(E/u).