Question

A coil of current-carrying Nichrome wire is immersed in a liquid. (Nichrome is a nickel–chromium–iron alloy commonly used in heating elements.) When the potential difference across the coil is 12 Vand the current through the coil is 5.2 A, the liquid evaporates at the steady rate of 21 mg/s. Calculate the heat of vaporization of the liquid (see Module 18-4).

Short answer

The heat of vaporization of the liquid is $3\times {10}^{6}J/kg$.

Step-by-step solution

The given data

1. Potential difference, V = 12V
2. Current, i = 5.2A
3. Mass rate, m/t = 21mg/s

Understanding the concept of the heat

To vaporize a liquid means to change it from the liquid state to the vapor (gas) state. Latent Heat of vaporization (L) is the amount of energy per unit mass that must be transferred as heat when the sample completely undergoes a phase change. Thus, when a Nichrome wire is immersed in a liquid of mass and latent heat of vaporization it supplies the heat to the liquid that completely undergoes a phase change. So, the total energy transferred is the latent heat of fusion. In this problem, the rate at which the heat is being supplied can be found by using the electric power formula.

Formulae:

Rate of change in heat, P = iV (i)

The latent heat of vaporization of a gas, L = Q/m (ii)

Step 3: Calculation of the heat of vaporization

The change in heat can be calculated using the given data in equation (i) as follows:

$$\begin{gathered} P=\left(5.2)\times (12\right) \\ =62.4W \end{gathered}$$

Now, amount of heat vaporized is calculated using the given values in equation (ii) as follows:

$\begin{array}{l}L=\frac{Pt}{m}\\ =\frac{62.4}{21\times {10}^{-6}}\\ =3\times {10}^{6}J/kg\end{array}$

Hence, the value of the heat of vaporization is $3\times {10}^{6}J/kg$.