A 20 g lead bullet leaves a rifle at a temperature of 47 degrees celcieus and travels at a velocity of 500 m/s until it hits a large block of ice at 0 degrees celcuis and comes to rest within it. How much ice will melt?
To determine the amount of ice that will melt when the lead bullet hits it, we need to calculate the energy transferred from the bullet to the ice. This can be done using the concepts of heat transfer and specific heat capacity.
First, let's calculate the initial kinetic energy of the bullet using the formula:
Kinetic energy = (1/2) * mass * velocity^2
Given:
Mass of the bullet (m) = 20 g = 0.02 kg
Velocity of the bullet (v) = 500 m/s
Kinetic energy of the bullet = (1/2) * 0.02 kg * (500 m/s)^2
Next, we need to determine the energy required to raise the temperature of the bullet from 47 degrees Celsius to its melting point, which is approximately 327 degrees Celsius for lead. We can use the specific heat capacity formula:
Energy = mass * specific heat capacity * temperature change
Given:
Mass of the bullet (m) = 20 g = 0.02 kg
Specific heat capacity of lead (c) = 130 J/kg°C
Initial temperature of the bullet (T1) = 47°C
Melting point temperature of lead (T2) = 327°C
Temperature change = T2 - T1
Energy required to raise the bullet's temperature = 0.02 kg * 130 J/kg°C * (327°C - 47°C)
Now, let's calculate the total energy transferred from the bullet to the ice. Since the bullet comes to rest inside the block of ice, the energy transferred will be equal to the sum of the initial kinetic energy and the energy required to raise the bullet's temperature:
Total energy transferred = Kinetic energy of the bullet + Energy required to raise its temperature
Finally, to determine the amount of ice that will melt, we need to convert this energy into heat by multiplying the total energy transferred by the specific heat capacity of ice. The specific heat capacity of ice is approximately 2100 J/kg°C.
Amount of ice melted = Total energy transferred / Specific heat capacity of ice
By following these steps and plugging in the given values, you can calculate the amount of ice that will melt when the lead bullet hits it.