Temperature and Radiation Energy

The rate of radiation energy emitted by an object is directly related to its temperature. This relationship is described by the Stefan-Boltzmann law, which states that the power radiated per unit area of a black body is proportional to the fourth power of its absolute temperature. The equation for this relationship is given by:

Q = σ * T^4

Where:
Q is the rate of radiation energy emitted in watts per square meter (W/m^2)
σ is the Stefan-Boltzmann constant (approximately 5.67 x 10^-8 W/m^2K^4)
T is the absolute temperature of the object in Kelvin (K)

Calculating the Rate of Radiation Energy

To calculate the rate of radiation energy emitted by the iron at a temperature of 27°C (300 K), we can use the given rate of radiation energy, Q = 1 kW/m^2.

Q = σ * T^4
1 = 5.67 x 10^-8 * (300)^4
1 = 5.67 x 10^-8 * 81 x 10^8
1 = 4.6 x 10^1

Therefore, the rate of radiation energy emitted by the iron at 27°C is approximately 46 W/m^2.

Calculating the Rate of Radiation Energy at a Higher Temperature

To find the rate of radiation energy emitted by the iron at a temperature of 151°C (424 K), we can use the same equation and substitute the new temperature value.

Q = σ * T^4
Q = 5.67 x 10^-8 * (424)^4
Q = 5.67 x 10^-8 * 81 x 10^16
Q = 3.68 x 10^9

Therefore, the rate of radiation energy emitted by the iron at 151°C is approximately 3.68 x 10^9 W/m^2.

Summary

- The rate of radiation energy emitted by an object is directly proportional to its temperature according to the Stefan-Boltzmann law.
- Using the given rate of radiation energy at 27°C, we can calculate the rate of radiation energy at 151°C using the Stefan-Boltzmann equation.
- The rate of radiation energy emitted by the iron at 27°C is approximately 46 W/m^2.
- The rate of radiation energy emitted by the iron at 151°C is approximately 3.68 x 10^9 W/m^2.