How fast must a lead bullet travel so that it melts when fired into a thick slab of wood, assuming that no heat is lost to the wood?(Assume initially that Tc=20 degrees Celsius)
**Im really confused on how to solve the problem.
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Assume the bullet is a solid piece of lead at temperature Tc traveling at velocity V. When the bullet comes to rest in the wood, assume all the kinetic energy of the bullet becomes heat, and no heat is lost to the wood. All that KE has to go somewhere, so we expect it will go into raising the temperature of the bullet, and carrying it through the phase transition from solid to liquid.
In order for the bullet to melt, enough energy must be imparted to
1) raise the temperature of the bullet to the melting point
2) supply the heat of fusion required to complete the phase change from solid to liquid at the melting point temperature.
The basic energy balance is then
KE = (1/2) (mass bullet) V^2 = (mass bullet) (specific heat of lead) (T_melting – Tc) + (mass bullet) (heat of fusion of lead)
Note that the mass of the bullet cancels out, so you just need to look up some thermodynamic properties of lead to solve the problem.
The information needed to solve this:
1. Calculate the bullet’s Energy = 1/2 (mass)(velocity)(velocity), in Joules.
2. Heat rise required = (melting point of lead) – 20 deg. C. = (327 – 20) deg. C = 307 deg. C
3. To calculate the heat rise of the bullet, use the specific heat of lead = 0.13 KJoules/(Kgram)(deg. C)