For a black body at temperature \(727^{\circ}C\), its radiating power is 60 watt and temperature of surrounding is \(227^{\circ}C\). If temperature of black body is changed to \(1227^{\circ}C\) then its radiating power will be:

Question

If current in a conductor \(3t^2 + 4t^3\), charge = \(?\), flow \(t = 1\; to\; t = 2s\)

Answer 1

To solve this problem, we need to use the concept of Stefan-Boltzmann Law, which describes the power radiated by a black body in terms of its temperature. The law is expressed by the equation:

P = \sigma A (T^4 - T_s^4)

Where:

P is the power radiated by the black body in watts.
\sigma is the Stefan-Boltzmann constant, approximately 5.67 \times 10^{-8} \, \text{Wm}^{-2}\text{K}^{-4}.
A is the surface area of the black body.
T is the absolute temperature of the black body in Kelvin.
T_s is the absolute temperature of the surroundings in Kelvin.

Given:

Initial temperature of the black body, T_1 = 727^\circ C = 1000 \, K
Surrounding temperature, T_s = 227^\circ C = 500 \, K
Initial radiating power, P_1 = 60 \, W

First, we calculate the radiating power using the Stefan-Boltzmann Law:

For the initial conditions,

P_1 = \sigma A (1000^4 - 500^4)

When the black body's temperature is increased to 1227^\circ C,

New temperature, T_2 = 1500 \, K

Using the same formula for new conditions:

P_2 = \sigma A (1500^4 - 500^4)

We relate the two power equations assuming the area and constant remain the same:

\dfrac{P_2}{P_1} = \dfrac{1500^4 - 500^4}{1000^4 - 500^4}

We know P_1 = 60 \, W.

Calculate:

P_2 = 60 \cdot \dfrac{1500^4 - 500^4}{1000^4 - 500^4}

After solving the equation (the detailed calculation of powers involves large numbers, best approached using a calculator), we find:

P_2 = 320 \, W

Therefore, the radiating power when the temperature of the black body is increased to 1227^\circ C is 320 W.

Answer 2