1) If we have a certain mass of liquid nitrogen, m , what is the heat Q needed t

Question

1) If we have a certain mass of liquid nitrogen, m, what is the heat Q needed to turn that mass into gas?

2) When liquid nitrogen is sitting in a room at room temperature, heat from the environment causes it to boil. The rate that this heat is absorbed by the nitrogen is DQe/Dt. The e subscript stands for environment. This rate has to equal the heat absorbed from question 1), divided by a change in time, Dt. Which of the terms from question 1) can change with time? Label the mass in this equation m1.

3) If we submerge an electrical resistor in the nitrogen and run current through it, then more heat is delivered to the nitrogen. The heat per time for an electrical resistor is DQr/Dt=V2/R, where V is the voltage across resistor, and R is the value of the resistance. In this situation, the heat delivered to the nitrogen is the sum of the environmental heat and the heat from the resistor. Write an equation similar to the answer to 2), this time also including the heat from the resistor. Label the mass in this equation m2.

4) The equations in 2) and 3) both contain an environment term. We want to eliminate that term since we don’t have a good way of measuring it, so subtract 2) from 3), and solve for Lv.

Explanation / Answer

1) for cvertain mass of liquid nitrogen m

let its temperature be Ti

its boiling temperature = Tb

heat capacity of liquid form = C

latent heat of vapouriosation = L

then

Q = mC(Tb - Ti) + mL

2) from 1

dQ/dt = C(Tb - T)dm/dt + Cm(-dT/dt)

3) dQr/dt = V^2/R

in this case

dQ/dt = C(Tb - T)dm2/dt + Cm2(-dT/dt) + V^2/R = dQe/dt

4) finally we get

dQ/dt = C(Tb - T)dm2/dt + Cm2(-dT/dt) + V^2/R

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