Warm objects emit electromagnetic radiation in the infrared...

Warm objects emit electromagnetic radiation in the infrared region. Heat lamps employ this principle to generate infrared radiation. Water absorbs infrared radiation with wavelengths near $2.80$ $\mu \mathrm{m}$. Suppose this radiation is absorbed by the water and converted to heat. A 1.00-L sample of water absorbs infrared radiation, and its temperature increases from $20.0^{\circ} \mathrm{C}$ to $30.0^{\circ} \mathrm{C}$. How many photons of this radiation are used to heat the water?

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Key Concepts

Calorimetry and Specific Heat

Calorimetry involves measuring the heat absorbed or released by a substance during a temperature change. The specific heat capacity of a substance is a measure of the amount of heat required to change the temperature of a unit mass by one degree, and it is used to calculate the total energy absorbed by the water when its temperature increases.

Infrared Radiation

Infrared radiation is a type of electromagnetic radiation with wavelengths longer than visible light. It is commonly associated with the thermal emission from objects, meaning that warmer objects emit more infrared radiation. This principle is used in various applications such as remote sensing, thermal imaging, and heat lamps.

Photon Energy and Planck’s Relation

The energy of a single photon is determined by its wavelength or frequency, as described by Planck’s equation E = hc/?, where E is energy, h is Planck’s constant, c is the speed of light, and ? is the wavelength. This concept is essential in quantifying how many photons are required to deliver a specific amount of energy.

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