A lead bullet moving at 204 m/s is stopped in a block of wood. All of the kinetic energy goes into heating the bullet. The initial temperature of the bullet is 25 degrees C. What is the final temperature of the bullet in degrees C
X DAE
To determine the final temperature of the bullet, we need to use the concept of specific heat and the conservation of energy.
1. Calculate the initial kinetic energy of the bullet:
- The formula for kinetic energy is KE = 0.5 * m * v^2, where KE is the kinetic energy, m is the mass of the bullet, and v is the velocity.
- Let's assume the mass of the bullet is 1 kg.
- The initial kinetic energy of the bullet is therefore KE = 0.5 * 1 kg * (204 m/s)^2 = 20,880 J.
2. Determine the specific heat capacity of lead:
- Specific heat capacity (C) is the amount of heat energy required to raise the temperature of a given substance by 1 degree Celsius.
- The specific heat capacity of lead is 129 J/kg°C.
3. Calculate the change in temperature:
- Since all the kinetic energy is converted into heat energy, we can equate the initial kinetic energy to the heat energy added to the bullet.
- The heat energy (Q) can be calculated using the formula Q = m * C * ΔT, where Q is the heat energy, m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.
- Rearranging the formula, ΔT = Q / (m * C).
- Substituting the known values, ΔT = 20,880 J / (1 kg * 129 J/kg°C).
4. Calculate the final temperature:
- Add the change in temperature to the initial temperature:
- Final temperature = Initial temperature + ΔT.
Let's perform the calculation to find the final temperature of the bullet.