What must be the initial velocity of a lead bullet at 25 degrees Celsius so that the heat developed when it is brought to rest will be sufficient to melt it at 327.3 degrees Celsius ?

To find the initial velocity of the lead bullet, we can use the principle of conservation of energy. The heat developed when the bullet is brought to rest is equal to the kinetic energy of the bullet when it was in motion.

The heat required to melt the lead bullet can be calculated using the formula:

Q = m * L

Where:
Q = heat required to melt the lead bullet
m = mass of the lead bullet
L = heat of fusion of lead (24.5 J/g)

The kinetic energy of the bullet can be calculated using the formula:

KE = 0.5 * m * v^2

Where:
KE = kinetic energy
m = mass of the lead bullet
v = initial velocity of the lead bullet

Since the heat developed when the bullet is brought to rest is equal to the kinetic energy of the bullet, we can set these two equations equal to each other:

0.5 * m * v^2 = m * L

Solving for v, we get:

v = sqrt(2 * L)

Substitute the values of L (24.5 J/g) and convert the temperature difference from Celsius to Kelvin (327.3 - 25 = 302.3 K), we get:

v = sqrt(2 * 24.5 J/g) = 7.85 m/s

Therefore, the initial velocity of the lead bullet must be 7.85 m/s in order for the heat developed when it is brought to rest to be sufficient to melt it at 327.3 degrees Celsius.