Question 10.5: A domestic microwave oven has a rated output of 600 W at 245......
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 \rho = 0.986 g/cm³
Specific heat C = 4.178 J/g °C
Dielectric constant \epsilon = 76.7
tan δ = 0.15
Now determine:
Field strength for water.
Power absorbed.
Comment on the result.
Consider the basic equation for microwave heating.
\frac{q}{V} = 0.556 \times 10^{-12} \times f E^2 \epsilon \tan δSubstituting for f, \epsilon, and tan d in L.H.S.
= 0.556 \times 10^{-12} \times E^2 \times 76.7 \times 0.15 \\ = 1.6 \times 10^{-2}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,
Solving for E
\begin{aligned}E & =\sqrt{\frac{210}{16 \times 10^{-2}}} \\& =110 \ \mathrm{~V} / \mathrm{cm}^2\end{aligned}Power absorbed by 200 cm water in 110 sec is
W=\frac{J}{t}=\frac{200 \times 210}{110} \\ = 380 \ WSimilar calculations for larger volumes of water produces the following results
\begin{array}{cc}\text { Volume }\left(\mathrm{cm}^3\right) & \text { Power to heat to } 80^{\circ} \mathrm{C} \\200 & 380 \\400 & 450 \\600 & 530 \\1000 & 530\left(68^{\circ} \mathrm{C}\right) \\1500 & 530\left(55^{\circ} \mathrm{C}\right)\end{array}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 (\epsilon, \tan δ) and of boiling at 100°C.