A 2.00 g lead bullet traveling at 650 m/s strikes a target, converting its kinetic energy into thermal energy. It's initial temperature is 40.0°C. Find the available kinetic energy of the bullet.
Find the heat required to melt the bullet
(both answers in J)
To find the available kinetic energy of the bullet, we can use the formula for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Given:
Mass of the bullet (m) = 2.00 g = 0.002 kg
Velocity of the bullet (v) = 650 m/s
Substituting these values into the formula, we get:
Kinetic Energy = (1/2) * 0.002 kg * (650 m/s)^2
Kinetic Energy = (1/2) * 0.002 kg * 422,500 m^2/s^2
Kinetic Energy = 422.5 J
Therefore, the available kinetic energy of the bullet is 422.5 J.
To find the heat required to melt the bullet, we need to calculate the heat energy required to increase the temperature of the bullet from its initial temperature to its melting point, and also the heat energy required to melt the bullet.
The specific heat capacity of lead is 130 J/kg·°C, and the melting point of lead is 327.5°C.
Step 1: Calculate the heat required to increase the temperature of the bullet. We will assume that the final temperature is equal to the melting point.
Heat required to increase the temperature = mass * specific heat capacity * change in temperature
Change in temperature = final temperature - initial temperature
= 327.5°C - 40.0°C
Substituting the values:
Change in temperature = 287.5°C = 287.5 K
Heat required to increase the temperature = 0.002 kg * 130 J/kg·°C * 287.5 K
Step 2: Calculate the heat required to melt the bullet.
Heat required to melt the bullet = mass * heat of fusion
Heat of fusion (for lead) = 23,900 J/kg
Heat required to melt the bullet = 0.002 kg * 23,900 J/kg
Adding the heat required for both steps will give the total heat required to melt the bullet:
Total heat required = Heat to increase the temperature + Heat to melt the bullet
Therefore, the heat required to melt the bullet is:
Total heat required = (0.002 kg * 130 J/kg·°C * 287.5 K) + (0.002 kg * 23,900 J/kg)
To find the available kinetic energy of the bullet, we can use the formula for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Given:
Mass of the bullet (m) = 2.00 g = 0.00200 kg
Velocity of the bullet (v) = 650 m/s
Plugging in these values into the formula, we get:
Kinetic Energy = (1/2) * 0.00200 kg * (650 m/s)^2
Simplifying the equation, we have:
Kinetic Energy = 0.5 * 0.00200 kg * (650 m/s)^2
Now, let's calculate the value:
Kinetic Energy = 0.5 * 0.00200 kg * (650 m/s)^2
= 0.5 * 0.00200 kg * 422,500 m^2/s^2
Multiplying the values gives:
Kinetic Energy ≈ 422.5 J
Therefore, the available kinetic energy of the bullet is approximately 422.5 Joules.
To find the heat required to melt the bullet, we need the specific heat capacity of lead (c) and the heat of fusion for lead (ΔHf).
Specific heat capacity of lead (c) = 0.129 J/g°C
Heat of fusion for lead (ΔHf) = 24.5 J/g
Given:
Mass of the bullet (m) = 2.00 g
To find the heat required to melt the bullet, we can use the formula:
Heat (Q) = mass * specific heat capacity * temperature change + mass * heat of fusion
First, let's calculate the temperature change:
Initial temperature (T_initial) = 40.0°C
Final temperature (T_final) = Melting point of lead = 327.5°C
Temperature change (ΔT) = T_final - T_initial
= 327.5°C - 40.0°C
= 287.5°C
Now, we can calculate the heat required to melt the bullet:
Heat (Q) = mass * specific heat capacity * temperature change + mass * heat of fusion
= 2.00 g * 0.129 J/g°C * 287.5°C + 2.00 g * 24.5 J/g
Multiplying the values gives:
Heat (Q) ≈ 74.01 J + 49 J
Therefore, the heat required to melt the bullet is approximately 123.01 Joules.