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Answer :
The power radiated by the radiator changes by a factor of 14.1573 when the temperature is increased from 27°C to 54°C.
The formula that relates the power radiated by an object with the fourth power of the temperature is known as the Stefan-Boltzmann Law. It is stated as follows: P = σA(T⁴), where P is the power radiated, σ is the Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²K⁴), A is the surface area of the radiator, and T is the temperature in Kelvin.
We must first convert the temperature to Kelvin:
TK = T°C + 273.15
TK1 = 27°C + 273.15 = 300.15 K
TK2 = 54°C + 273.15 = 327.15 K
The factor by which the power radiated changes is the ratio of the power at the new temperature to the power at the original temperature. The equation is as follows:
P2/P1 = (T2/T1)⁴
Substituting the given values:
P2/P1 = (327.15/300.15)⁴
P2/P1 = 1.8856⁴
P2/P1 = 14.1573
You can learn more about the temperature at: brainly.com/question/7510619
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