A lead bullet with a mass of 0.05 kg traveling at 188 m/s strikes an armor plate and comes to a stop. If all the energy is converted to heat and absorbed by the bullet, what is the temperature change?
mv²/2 =mcΔT
for lead c =130 J/kg•K
ΔT= v²•c/2= 188²/2•130=135º
To calculate the temperature change, we need to use the equation for heat transfer. The equation is:
Q = mcΔT
Where:
Q is the heat transferred
m is the mass of the bullet
c is the specific heat capacity of the bullet
ΔT is the change in temperature
First, we need to calculate the heat transferred (Q). Since all of the energy is converted to heat and absorbed by the bullet, the heat transferred is equal to the kinetic energy of the bullet before it stops. The kinetic energy (KE) can be calculated using the formula:
KE = 0.5 * m * (velocity)^2
In this case, mass (m) is given as 0.05 kg and velocity is given as 188 m/s. Plugging these values into the formula, we get:
KE = 0.5 * 0.05 kg * (188 m/s)^2
Now we have the value for kinetic energy (KE). Next, we need to find the specific heat capacity of the bullet (c). The specific heat capacity is a material-specific value that tells us how much heat energy is required to raise the temperature of a unit mass of the material by one degree Celsius. This value may vary depending on the material of the bullet.
Let's assume a specific heat capacity of 0.140 J/g°C for lead, which can also be represented as 140 J/kg°C.
Now we can calculate the temperature change (ΔT). Rearranging the formula Q = mcΔT, we get:
ΔT = Q / (mc)
Plugging in the values for Q (calculated previously), m (0.05 kg), and c (140 J/kg°C), we can now calculate the temperature change (ΔT).
ΔT = KE / (m * c)
Keep in mind that the specific heat capacity values may vary depending on the material.