Question

Assuming that 50% of the initial kinetic energy of the bullet is converted into thermal energy in the bullet and the specific heat of lead is c, write an expression that would allow you to determine the bullet's temperature increase. Express your answer in terms of some or all of the variables: m, vi, and c.

Answer 1

Answer:

$\Delta T=\frac{v_{i}^{2}}{4c}$

Explanation:

Let the mass of bullet is m, initial velocity of bullet is vi and c be the specific heat of the bullet.

Kinetic energy, K = 1/2 mvi^2

According to the question, 50% of the kinetic energy is equal to the heat energy absorbed by the bullet.

50% of K = mass of bullet x specific heat x rise in temperature

1/4 mvi^2 = m x c x ΔT

$\Delta T=\frac{v_{i}^{2}}{4c}$