Photons of infrared radiation are responsible for much of...

Photons of infrared radiation are responsible for much of the warmth we feel when holding our hands before a fire. These photons will also warm other objects. How many infrared photons with a wavelength of $1.5 \times 10^{-6} \mathrm{m}$ must be absorbed by the water to warm a cup of water (175 g) from $25.0^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C} ?$

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Key Concepts

Specific Heat Capacity

This concept refers to the amount of energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or one Kelvin). It is a fundamental property used in calculating the energy needed to change the temperature of a substance, expressed by the equation Q = m * c * ?T, where Q is the heat energy, m is mass, c is the specific heat capacity, and ?T is the temperature change.

Photon Energy

Photon energy is the energy carried by a single photon of electromagnetic radiation. It is determined using the equation E = (h * c) / ?, where E is the energy, h is Planck's constant, c is the speed of light, and ? is the wavelength. This relationship shows that photon energy is inversely proportional to its wavelength.

Radiation Absorption and Energy Conversion

This concept involves the process by which matter absorbs energy from electromagnetic radiation. When photons are absorbed by a substance, their energy is converted into thermal energy, increasing the substance’s internal energy and potentially raising its temperature. This process is central to understanding how radiation results in heating effects.

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