To illustrate means to explain or clarify a concept using examples, diagrams, or visual aids. It helps make abstract ideas more understandable. For instance, to illustrate the concept of thermal expansion, one could show a metal rod expanding when heated or demonstrate how the length of a liquid increases in a thermometer.
Chapter 10 of Class 11 Physics focuses on thermal properties of matter. It covers topics like temperature and heat and thermal expansion and specific heat capacity and calorimetry. The chapter also explains heat transfer methods such as conduction and convection and radiation. Additionally it discusses laws of thermodynamics and ideal gas laws.
Wien’s Displacement Law states that the wavelength (λ_max) at which the intensity of radiation emitted by a black body is maximum is inversely proportional to its absolute temperature (T). In other words, as the temperature of the black body increases, the wavelength at which it emits the most radiation decreases.
Mathematically, Wien’s Displacement Law is given as:
λ_max = b / T
where:
– λ_max is the wavelength at which the emission intensity is maximum,
– T is the absolute temperature of the black body in Kelvin (K),
– b is Wien’s displacement constant, approximately 2.898 × 10⁻³ m·K.
Illustration:
– Object at 300 K: Using Wien’s Displacement Law, we calculate the wavelength where its radiation peaks.
λ_max = (2.898 × 10⁻³) / 300 = 9.66 μm
This is in the infrared region.
– Object at 600 K: The peak wavelength of emission is twice the object at 300 K since the temperature has an inverse proportionality to peak wavelength.
λ_max = (2.898 × 10⁻³) / 600 = 4.83 μm
It is still within the infrared, but shorter now.
Relevance of Wien’s Displacement Law:
1. Temperature Determination from Radiation:
Temperature of any object could be determined by the peak wavelength of emitted radiation under the law. It finds many applications in astrophysics, for example, to estimate the temperature of stars as a function of the color of stars. Therefore, it gives a color equivalent estimation.
2. Color of Stars
According to Wien’s law, hotter stars emit more radiation at shorter wavelengths, causing them to appear bluer, and cooler stars emit at longer wavelengths, making them appear redder.
3. Thermal Radiation Understanding:
Wien’s law helps us understand the nature of thermal radiation and how temperature affects the radiation emitted by objects, which is vital in many fields, including climatology and energy studies.
4. Temperature Measurement Applications: The law is applied in infrared thermometry, which allows objects to be measured for temperature without direct contact. This is found in industrial, medical, and scientific applications.
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