A domestic microwave oven has a rated output of 600 W at 2450 MHz. Experiments were conducted by heating various quantities of water initially at 30°C. The temperature of water was measured after heating for different lengths of time. The results are shown in Figure 10.17. Water has following

Question

A domestic microwave oven has a rated output of 600 W at 2450 MHz.

Experiments were conducted by heating various quantities of water initially at 30°C. The temperature of water was measured after heating for different lengths of time. The results are shown in Figure 10.17.

Water has following related properties (assumed constant):

Density [latex]\rho[/latex] = 0.986 g/cm³
Specific heat C = 4.178 J/g °C
Dielectric constant [latex]\epsilon[/latex] = 76.7
tan δ = 0.15

Now determine:
Field strength for water.
Power absorbed.
Comment on the result.

Accepted Answer

Consider the basic equation for microwave heating.

[latex]\frac{q}{V} = 0.556 imes 10^{-12} imes f E^2 \epsilon an δ[/latex]

Substituting for [latex]f, \epsilon[/latex], and tan d in L.H.S.

[latex]= 0.556 imes 10^{-12} imes E^2 imes 76.7 imes 0.15 \ = 1.6 imes 10^{-2}[/latex]

The field strength E (V/cm²) is not known.
The experimental data show that 200 cm (~ 200 g) of water was heated to 80°C in 110 sec.
Hence,

[latex] \begin{aligned}\frac{q}{V} & =\frac{200 imes 0.986 imes 4.178 imes(80-30)}{200} \& =210 \ \mathrm{~J} / \mathrm{cm}^3 \& =1.6 imes 10^{-2} ext { as calculated above. }\end{aligned} [/latex]

Solving for E

[latex]\begin{aligned}E & =\sqrt{\frac{210}{16 imes 10^{-2}}} \& =110 \ \mathrm{~V} / \mathrm{cm}^2\end{aligned}[/latex]

Power absorbed by 200 cm water in 110 sec is

[latex]W=\frac{J}{t}=\frac{200 imes 210}{110} \ = 380 \ W[/latex]

Similar calculations for larger volumes of water produces the following results

[latex]\begin{array}{cc} ext { Volume }\left(\mathrm{cm}^3 ight) & ext { Power to heat to } 80^{\circ} \mathrm{C} \200 & 380 \400 & 450 \600 & 530 \1000 & 530\left(68^{\circ} \mathrm{C} ight) \1500 & 530\left(55^{\circ} \mathrm{C} ight)\end{array}[/latex]

The above results show that the oven capacity (~ 600 W) limits the maximum quantity of water that can be heated to 80°C in less than 5 min and to about 600 cm³.
For quantities about 200–400 cm, the power absorbed is limited by the electrical constants ([latex]\epsilon, an δ[/latex]) and of boiling at 100°C.

Question 10.5: A domestic microwave oven has a rated output of 600 W at 245......

Related Answered Questions

Determine the depth of penetration for 0.4% carbon steel heated from 30–900°C at 1000 Hz. The resistivity and permeability at various temperatures is given below. ...

Verified Answer:

Verified Answer:

Determine the frequency range for through heating aluminum bar 0.02 m diameter to 500°C. The average resistivity of aluminum is 5.83 × 10^−8 ohm.m. What will be the frequency range if the bar diameter is 0.01 and 0.1 m? ...

Verified Answer:

What will be the depth of penetration of a nonferrous alloy heated from 30–600°C at 10,000 Hz. The resistivity of the alloy is same as that of steel in the previous problem. ...

Verified Answer: