A law is a fundamental principle or rule that describes natural phenomena consistently observed under specific conditions. In science, laws are derived from empirical evidence and experimentation. They are universally accepted and can predict outcomes, such as Newton’s laws of motion or the laws of thermodynamics.
Chapter 10 of Class 11 Physics deals with thermal properties of matter. It explains concepts like temperature and heat and thermal expansion and specific heat capacity and calorimetry. The chapter also covers heat transfer methods such as conduction and convection and radiation. It further discusses laws of thermodynamics and ideal gas laws.
The power radiated by a black body is proportional to the fourth power of its absolute temperature:
P = σ A T⁴
where:
– P: Power radiated
– σ: Stefan-Boltzmann constant
– A: Surface area of the body
– T: Absolute temperature of the body
If the body is in an environment at temperature Tₑ, the net radiated power becomes:
P_net = σ A (T⁴ – Tₑ⁴)
Approximation for Small Temperature Differences:
For T ≈ Tₑ, expand T⁴ – Tₑ⁴ using the binomial approximation:
T⁴ – Tₑ⁴ ≈ 4 Tₑ³ (T – Tₑ)
Substituting into the net power equation:
P_net = σ A ⋅ 4 Tₑ³ (T – Tₑ)
Regarding Newton’s Law of Cooling:
Newton’s Law of Cooling reads: \dT/dt = -k (T – Tₑ) where k is a proportionality constant.
In the above equation:
P_net = σ A ⋅ 4 Tₑ³ (T – Tₑ)
If P_net is proportional to the rate of temperature change dT/dt:
k = (σ A ⋅ 4 Tₑ³) / (m c) where:
– m: Mass of the body .
-c: Specific heat capacity .
Therefore, in the limiting situation where temperature difference is negligible, the Stefan-Boltzmann Law becomes the Newton’s Law of Cooling.
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