Given a change in internal energy, how can I find the temperatur

1. The problem statement, all variables and given/known data
Two speeding lead bullets, one of mass 15.0 g moving to the right at 270 m/s and one of mass 7.65 g moving to the left at 390 m/s, collide head-on, and all the material sticks together. Both bullets are originally at temperature 30.0°C. Assume the change in kinetic energy of the system appears entirely as increased internal energy. We would like to determine the temperature and phase of the bullets after the collision. (Lead has a specific heat of 128 J/(kg K), a melting point of 327.3°C, and a latent heat of fusion of 2.45 104 J/kg.)

(e) What is the temperature of the combined bullets after the collision?

(f) What is the phase of the combined bullets after the collision?
mbullet,solid= ____ g
mbullet,liquid= ____ g

2. Relevant equations

I have already correctly found the change in internal energy to be 1098J.


3. The attempt at a solution

I really don’t know how to do this.

I tried finding the heat required to raise the temperature from 30C to the melting point using Q=mc[itex]\Delta[/itex]T => Q=.0226kg*128J/(kgK)*297.3K and found this to be 860J but I don’t know where to go from there.

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