Impulse Momentum + Thermal Physics

A 150 g bullet made of ice at 0 degrees Celsius is shot from a gun and travels at 500 m/s before embedding itself in a block of wood.

(a) If the bullet's kinetic energy is totally converted to heat that it also absorbs, how much ice melts?

(b) Take that same energy and assume that give moles of an ideal gas at room temperature (20 degrees Celsius) do that much work while expanding at constant pressure.

i. What is the change in volume of the gas?

ii. What is the final temperature of the gas?

(c) What is the Carnot efficiency of an engine operating between these two temperatures?

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Okay, so I've been told $\displaystyle Q = KE = (1/2) * m * v^2$

I assume that g needs to be kg.

So $\displaystyle (1/2)*(.15)*(500)^2 = 18,750 J/kg$

Now at this point I think I need to do C*M*DeltaT but I'm not sure how to get Delta T.

I know this is a lot of work, but any help would be appreciated, if anyone would like to push me in the right direction.

(I really hate to be down on teachers, as it is normally the students fault, but my physics teacher basically hands us homework and tells us to figure it out. And you guys on this forum have been a tremendous help.)