Question

. The density of ice is 917 kg/m3, and the latent heat of fusion of water is 3.35 x 105 J/kg. The driver of the van turns on the rear-window defroster, which operates at 12 V and 29 A. The defroster directly heats an area of 0.56 m2 of the rear window. What is the maximum thickness of ice above this area that the defroster can melt in 3.8 minutes?

Answer 1

Max thickness; h = 4.61 x 10^(-4) m

Step-by-step explanation:

We are given;

Current; I = 29A

Voltage; V = 12 V

Time; t = 3.8 minutes = 228 seconds

Density;ρ = 917 kg/m³

latent heat of fusion of water; L = 3.35 x 10^(5) J/kg

Area; A = 0.56 m²

We know that volume = Area x Height.

Thus, V = Ah and h = V/A

We also know that density is given by;

ρ = mass/volume = m/V

Amd V = m/ρ

Thus, h can be written as;

h = (m/ρ)/A - - - - - (eq1)

Now, we know that;

The specific latent heat (L) of a material is a measure of the heat energy (Q) per mass (m) released or absorbed during a phase change.

It is defined through the formula

Q = mL

Thus, m = Q/L

So, putting Q/L for m in eq 1,we have; h = (Q/Lρ)/A = Q/LρA

Now, power(P) is; Q/t where Q is energy dissipated and t is time.

Thus, P = Q/t and thus, Q = Pt

Thus, h = Pt/LρA - - - - (eq2)

We also know that Power = IV

Thus, power = 29 x 12 = 348 W

Thus, plugging in the relevant values into eq(2),we have;

h = (348 x 228)/(3.35 x 10^(5) x 917 x 0.56)

h = 79344/(1720.292 x 10^(5))

h = 4.61 x 10^(-4) m

Answer 2

`s = 1.472\,m`

Step-by-step explanation:

The heat require to melt the ice formed in the rear window is:

`Q = m_(ice)\cdot L_(f)`

`Q = \rho_(ice)\cdot V_(ice)\cdot L_(f)`

`Q = \rho_(ice)\cdot A_(w)\cdot s \cdot L_(f)`

The heat transfer rate given by the defroster is:

`\dot Q = \epsilon\cdot i`

But:

`\epsilon \cdot i \cdot \Delta t = \rho_(ice)\cdot A_(w)\cdot s \cdot L_(f)`

The maximum thickness of ice that can be melt is:

`s = (\epsilon \cdot i \cdot \Delta t)/(\rho_(ice)\cdot A_(w)\cdot L_(f))`

`s = ((12\,V)\cdot (29\,A)\cdot (3.8\,min)\cdot ((60\,s)/(1\,min) ))/((917\,(kg)/(m^(3)) )\cdot (0.56\,m^(2))\cdot (105\,(J)/(kg) ))`

`s = 1.472\,m`