91Ó°ÊÓ

Microwave ovens are common household appliances known for their ability to quickly heat food and beverages. This happens through a process called energy conversion. In simple terms, energy conversion involves transforming one form of energy into another. In the case of microwaves, electrical energy is converted into microwave energy that then interacts with water molecules in food to generate heat.

This process is crucial, as it dictates the heating efficiency of the microwave oven. Most of the microwave's energy successfully converts into thermal energy, but some is lost in the form of heat dissipation or reflection. For example, in this exercise, only 92% of the microwave's energy effectively heats the water. Understanding this concept of energy conversion helps in evaluating the effectiveness and energy consumption of a microwave oven in practical applications.

Thermal energy refers to the internal energy present in a system due to its temperature. When you heat water, you are essentially increasing its thermal energy. The formula used to calculate the energy needed to change the temperature of a substance is given by:

• \( q = mc\Delta T \)

In this equation, \( m \) is the mass of the substance, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.

For water, the specific heat capacity is 4.18 J/g°C, which means it can absorb a significant amount of heat before its temperature rises. When you apply this formula to heat 150 mL (or grams) of water from 20°C to 100°C, you calculate that 50,160 Joules of thermal energy is necessary. This is the energy required to increase the water’s thermal store, using the energy conversion pathway previously mentioned.

Planck's constant is a fundamental physical constant that plays a vital role in quantum mechanics. It is the proportionality factor between the minimal increment of energy, a photon, and the frequency of its associated electromagnetic wave. Represented as \( h \), Planck's constant has the value \( 6.626 \times 10^{-34} \text{ Js} \).

This constant is critical when calculating the energy of a photon. Using the equation \( E = \frac{hc}{\lambda} \), where \( E \) is the energy of the photon, \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength, you can determine just how much energy a single photon carries. This constant suggests that energy and frequency are directly related, emphasizing the discrete nature of electromagnetic radiation, including microwaves seen in everyday appliances.

Calculating the number of photons involved in heating processes, such as in a microwave, involves quantifying how many individual packets of energy (photons) are needed. A single photon's energy is determined using the equation \( E = \frac{hc}{\lambda} \), which you've learned previously.

In our exercise, with a wavelength of \( 1.22 \times 10^8 \text{ nm} \), the energy of one photon comes out to \( 1.63 \times 10^{-24} \text{ J} \). To determine how many photons are needed to deliver the sufficient energy (54,521.74 Joules) to heat the water, you can use:

• \( N = \frac{\text{Total Energy}}{\text{Energy per Photon}} \)

This leads to required photon count calculated as approximately \( 3.34 \times 10^{28} \) photons. Understanding photon calculations helps bridge the gap between microscopic quantum events and macroscopic results, such as a hot cup of tea from microwave heating.