A microwave oven can heat 350 g of water from 25.0^∘ C to 100.0^∘ C in 2.00 min. (a) At what rat

step 1 The rate of energy absorption is delta Q over delta T. In this particular case, delta Q is the h

A microwave oven can heat 350 g of water from 25.0^∘ C to...

A microwave oven can heat 350 g of water from $25.0^{\circ} \mathrm{C}$ to $100.0^{\circ} \mathrm{C}$ in 2.00 min. (a) At what rate is energy absorbed by the water? (b) Microwaves pass through a waveguide of cross-sectional area $88.0 \mathrm{cm}^{2} .$ What is the average intensity of the microwaves in the wave guide? (c) What are the rms electric and magnetic fields inside the wave guide?

A microwave oven can heat 350 g of water from $25.0^{\circ} \mathrm{C}$ to $100.0^{\circ} \mathrm{C}$ in 2.00 min. (a) At what rate is energy absorbed by the water? (b) Microwaves pass through a waveguide of cross-sectional area $88.0 \mathrm{cm}^{2} .$ What is the average intensity of the microwaves in the wave guide?
(c) What are the rms electric and magnetic fields inside the wave guide?

Key Concepts

Specific Heat Capacity

This concept involves the amount of energy needed to raise the temperature of a unit mass of a substance by one degree Celsius. It is fundamental in calculating the energy required for heating or cooling a substance, using the relation Q = m × c × ?T, where Q is the heat energy, m is mass, c is the specific heat capacity, and ?T is the change in temperature.

Rate of Energy Transfer (Power)

Power is defined as the amount of energy transferred per unit time. In thermal processes and many other systems, it quantifies how fast energy is absorbed or delivered, and is calculated by dividing the total energy change by the time interval over which the change occurs.

Intensity of Electromagnetic Radiation

Intensity represents the power transmitted per unit area perpendicular to the direction of the wave propagation. It is a key concept in understanding how energy is distributed in a wave, and is critical in applications such as determining the energy flux in microwave systems or other electromagnetic radiation scenarios.

Relationship Between Intensity and Electromagnetic Fields

In electromagnetic theory, the intensity of a wave is directly related to the amplitudes of its electric and magnetic fields. Specifically, for electromagnetic waves in free space, the intensity can be expressed in terms of the root mean square (rms) electric field (and similarly the rms magnetic field) using relations that involve the permittivity of free space and the speed of light.

Root Mean Square (RMS) Values

The rms value is a statistical measure that represents the effective magnitude of a varying quantity, such as an oscillating electric or magnetic field. For sinusoidal waves, the rms value is equal to the peak value divided by the square root of two. It is particularly useful in calculating power or intensity because it directly relates to the average energy carried by the wave.

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