A 0.02 kg-lead bullet traveling 200 m/s strikes an armor plate and comes to a stop. If all of it's energy is converted to heat that it absorbs, what is the temperature change?
(1/2)MV^2 = M C*(delta T)
Mass M cancels out. C is the specific heat of lead.
Solve for the temperature change, delta T
delta T = V^2/(2*C)
The specific heat C must have units of
Joules/(kg*degC). Don't use units based on calories
Well, let's heat things up with some calculations! To find the temperature change, we'll be using the formula for heat energy, which is given by:
Q = mcΔT
Where:
Q is the heat energy
m is the mass of the bullet
c is the specific heat capacity of lead
ΔT is the change in temperature
First, let's find the heat energy. Since the bullet comes to a stop, all of its kinetic energy is converted into heat energy. The formula for kinetic energy is:
KE = (1/2)mv²
Where:
KE is the kinetic energy
m is the mass of the bullet
v is the velocity of the bullet
Now, let's calculate the kinetic energy:
KE = (1/2)mv²
KE = (1/2)(0.02 kg)(200 m/s)²
Solving that, we get:
KE = 400 J
Now, let's figure out the change in temperature. To do that, we'll use the formula:
Q = mcΔT
We already know Q is 400 J, m is 0.02 kg, and c is the specific heat capacity of lead. The specific heat capacity of lead is approximately 130 J/kg°C.
400 J = (0.02 kg)(130 J/kg°C)ΔT
Simplifying that, we get:
ΔT = 400 J / (0.02 kg)(130 J/kg°C)
ΔT ≈ 153.85 °C
So, if all of the energy is converted into heat, the temperature change of the lead bullet would be approximately 153.85°C. That's certainly a bullet that's got some heat!
To calculate the temperature change, we need to determine the amount of energy transferred to the bullet and then use the specific heat capacity of lead to calculate the temperature change.
Step 1: Calculate the kinetic energy of the bullet.
The kinetic energy (KE) of an object is given by the formula KE = (1/2) * m * v^2, where m is the mass and v is the velocity.
Given:
Mass (m) of the bullet = 0.02 kg
Velocity (v) of the bullet = 200 m/s
Using the formula, we can calculate the kinetic energy:
KE = (1/2) * 0.02 kg * (200 m/s)^2
= 0.02 kg * 20,000 m^2/s^2
= 400 J
Step 2: Calculate the temperature change using specific heat capacity.
The specific heat capacity (c) of lead is approximately 128 J/kg°C. This means that it takes 128 Joules to raise the temperature of 1 kg of lead by 1 degree Celsius.
Given:
Mass (m) of the bullet = 0.02 kg
Energy transferred (E) = 400 J
Using the formula, we can calculate the temperature change:
E = m * c * ΔT
400 J = 0.02 kg * 128 J/kg°C * ΔT
ΔT = 400 J / (0.02 kg * 128 J/kg°C)
ΔT = 156.25 °C
Therefore, the temperature change of the lead bullet, if all its energy is converted to heat, is approximately 156.25 °C.
To solve this problem, we need to use the law of conservation of energy. The bullet's initial kinetic energy will be converted into heat energy, causing a change in temperature. The equation that relates the change in temperature to the heat energy is:
Q = mcΔT
Where:
Q is the heat energy
m is the mass of the bullet
c is the specific heat capacity of lead
ΔT is the change in temperature
First, let's find the initial kinetic energy of the bullet:
Kinetic energy (KE) = 0.5 * m * v^2
Where:
m is the mass of the bullet (0.02 kg)
v is the velocity of the bullet (200 m/s)
KE = 0.5 * 0.02 kg * (200 m/s)^2
KE = 400 J
Now, we know that this kinetic energy will be converted into heat energy. The specific heat capacity of lead (c) is approximately 130 J/kg°C.
Using the equation Q = mcΔT, we can rearrange it to solve for ΔT:
ΔT = Q / mc
Substituting the known values:
ΔT = 400 J / (0.02 kg * 130 J/kg°C)
ΔT ≈ 15.38°C
Therefore, the temperature change of the bullet when it comes to a stop and all its kinetic energy is converted to heat energy is approximately 15.38 degrees Celsius.