Problem One:

"A 20-g lead bullet at 30 ºC and moving at 350 m/s embeds itself in a wooden block. (a) If 70% of the initial kinetic energy becomes internal energy of the bullet, what is its final temperature? (b) Does any of it melt? If so, how much?"

(a) J

ºC; ºC

However, the melting point of lead is 327 ºC. At that point, there is a Latent Heat of Fusion of 245000 J/kg, which is 490 J for the bullet's particular mass, required before the entire body will have changed phase to liquid. The heat actually transferred to the bullet is then only enough to raise it to 327 ºC, its final temperature.

(b) Because the heat transfer does exceed the amount needed to raise the bullet to 327 ºC, some of the bullet does melt. The portion that melts is proportional to the fraction of the Latent Heat of Fusion, above melting temperature, actually transferred.

Heat needed to raise the bullet from 30º to 327º is J.

;

17.4% of 20 grams is 3.48 grams, the portion of the bullet that melts.

Problem Two:

"One kilogram of water at 0 ºC and 1 atm freezes to ice at the same temperature. How much work is done by the water? The density of the liquid is 1000 kg/m³, and of ice it is 920."

The relationship of density, mass, and volume is such that . In this problem, the mass stays the same, so the volume increases in inverse proportion to the density decrease, entailing work.

m³; m³

m³

(1 atm) J