Answer:
To determine the initial speed of a lead bullet that must be at a temperature of 22.0 ∘C so that the heat developed when it is brought to rest will be just sufficient to melt it, you would need to use the equation for the change in internal energy of a system, which is ΔU = Q + W. In this case, the internal energy of the bullet will increase as it slows down and comes to a stop, and this increase in internal energy will be equal to the heat added to the bullet plus the work done on the bullet.
Since the bullet is not in contact with any external heat source and all the initial mechanical energy of the bullet is converted to heat, we can assume Q = -W.
In this case, the work done on the bullet is given by W = -1/2 * m * v^2, where m is the mass of the bullet and v is its initial velocity.
To melt the bullet we need to know the heat of fusion of lead, it is around 3.98 x 10^5 J/kg.
Therefore, the mass of the bullet and the heat of fusion can be used to determine the initial velocity of the bullet, we need to solve the equation
Q + W = m * Lf = -1/2 * m * v^2 = m * Lf
v = √(2 * Lf * m)
Note that, Lf is heat of fusion and m is the mass of the bullet
Please note that, this is a rough estimate and it's not taking into account many other factors such as the shape of the bullet, the cooling effect of the air, etc.