A3.00-kg block of copper at 23.0°c is dropped into a large vessel of liquid nitrogen at 77.3 k. how many kilograms of nitrogen boil away by the time the copper reaches 77.3 k? (the specific heat of copper is 0.092 0 cal/g · °c, and the latent heat of vaporization of nitrogen is 48.0 cal/g.)

1.2584kg of nitrogen boils.

Explanation:

Consider the energy balance for the overall process. There are not heat or work fluxes to the system, so the total energy keeps the same.

For the explanation, the 1 and 2 subscripts will mean initial and final state, and C and N2 superscripts will mean copper and nitrogen respectively; also, liq and vap will mean liquid and vapor phase respectively.

The overall energy balance for the whole system is:

The state 1 is just composed by two phases, the solid copper and the liquid nitrogen, so:

The state 2 is, by the other hand, composed by three phases, solid copper, liquid nitrogen and vapor nitrogen, so:

So, the overall energy balance is:

Reorganizing,

The left part of the equation can be written in terms of the copper Cp because for solids and liquids Cp≅Cv. The right part of the equation is written in terms of masses and specific internal energy:

Take in mind that, for the mass balance for nitrogen, ,

So, let's replace in the energy balance:

So, as you can see, the term disappear because (The specific energy in the liquid is the same because the temperature does not change).

The difference is the latent heat of vaporization because is the specific energy difference between the vapor and the liquid phases, so: