A certain microwave oven delivers 750 . watts (J / s) of power to a coffee cup containing 50.0

step 1 So in this problem, first of all, we are going to figure out the energy that's needed to heat th

A certain microwave oven delivers 750 . watts (J / s) of...

A certain microwave oven delivers $750 .$ watts $(\mathrm{J} / \mathrm{s})$ of power to a coffee cup containing $50.0 \mathrm{~g}$ water at $25.0^{\circ} \mathrm{C}$. If the wavelength of microwaves in the oven is $9.75 \mathrm{~cm}$, how long does it take, and how many photons must be absorbed, to make the water boil? The specific heat capacity of water is $4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$ and assume only the water absorbs the energy of the microwaves.

Key Concepts

Energy Transfer (Heating)

This concept involves the calculation of the total amount of energy required to raise the temperature of a substance. It typically makes use of the formula Q = m·c·?T, where Q is the energy required, m is the mass of the substance, c is its specific heat capacity, and ?T is the temperature change. This formula is fundamental in thermodynamics and helps quantify the energy needed during heating or cooling processes.

Power and Energy Relationship

Power is defined as the rate at which energy is transferred or converted per unit time, typically measured in joules per second (watts). The relationship between power (P), energy (E), and time (t) is given by the equation P = E/t. This concept allows for determining how long a specific energy transfer will take when the power input is known.

Specific Heat Capacity

Specific heat capacity is a material property that indicates how much energy is required to raise the temperature of a unit mass of a substance by one degree Celsius. It is a crucial concept in calorimetry and thermal physics because it determines the thermal response of substances when energy is added or removed.

Photon Energy

Photon energy refers to the discrete amount of energy carried by a photon in electromagnetic radiation. It is determined by the photon's frequency or wavelength. This concept is key in quantum mechanics and is used to calculate the energy contribution of individual photons to processes such as heating or chemical reactions.

Planck’s Equation

Planck’s Equation, E = (h*c)/?, connects a photon's energy (E) with its wavelength (?), where h is Planck's constant and c is the speed of light. This equation underpins quantum theory and describes how the energy of electromagnetic radiation is quantized, making it essential for understanding interactions between radiation and matter.

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