A 1.00 g lead bullet at 28.0°C is fired at a speed of 230 m/s into a large block of ice at 0°C, in which it becomes embedded. What quantity of ice melts?
Can someone walk me through this step by step?
The bullet will be brought down in temperature from 28 C to 0 C. That will add heat to the ice equal to
M*Clead*28 = 0.868 calories
where Clead is the specific heat of lead,0.031 cal/(g C)
In addition to this, the kinetic energy of the bullet, will be converted to heat, equal to
m V^2/2 = 0.001 kg*230^2/2 = 26.45 J = 6.33 calories
Total heat added to ice = 6.33 + 0.87 = 7.20 calories
Divide that by the heat of fusion of ice, 80 cal/g, to find out how much ice melts. Not very much, apparently.
Sure! Let's break it down step by step:
Step 1: Calculate the initial thermal energy of the lead bullet.
The initial thermal energy of the lead bullet can be calculated using the formula:
Q = mcΔT
Where:
- Q is the thermal energy
- m is the mass of the bullet
- c is the specific heat capacity of lead (0.13 J/g°C)
- ΔT is the change in temperature
In this case, the mass of the bullet, m, is given as 1.00 g, and the change in temperature, ΔT, is the initial temperature of the bullet (28.0°C) minus the final temperature (0°C). Plug in these values to calculate the initial thermal energy.
Step 2: Calculate the kinetic energy of the bullet.
The kinetic energy of an object can be calculated using the formula:
KE = 1/2mv^2
Where:
- KE is the kinetic energy
- m is the mass of the bullet
- v is the velocity of the bullet
In this case, the mass of the bullet, m, is given as 1.00 g, and the velocity, v, is given as 230 m/s. Plug in these values to calculate the kinetic energy.
Step 3: Calculate the amount of ice melted.
The energy required to melt a given mass of ice can be calculated using the formula:
Q = mL
Where:
- Q is the thermal energy required
- m is the mass of ice to be melted
- L is the latent heat of fusion of ice (334 J/g)
To calculate the amount of ice melted, we need to equate the thermal energy gained by the bullet (from Step 1) and the kinetic energy of the bullet (from Step 2) to the thermal energy required to melt the ice. Set the equations equal to each other and solve for the mass of ice, m.
Step 4: Convert the mass of ice from grams to a more practical unit, such as kilograms (kg), if needed.
That's it! By following these steps, you should be able to calculate the quantity of ice melted.