Final answer:
The power radiated by the tungsten sphere can be calculated using the Stefan-Boltzmann Law. By plugging in the values for emissivity, surface area, and temperature, we can determine the power to be approximately 182.44 watts.
Step-by-step explanation:
The power radiated by a spherical object can be calculated using the Stefan-Boltzmann Law, which states that the power radiated is proportional to the emissivity (e), the surface area (A), and the fourth power of the absolute temperature (T). The formula is given by:
P = eAT4
Where P is the power, e is the emissivity, A is the surface area, and T is the absolute temperature in Kelvin.
In this case, we have an emissivity of 0.35, a radius of 17 cm (which gives us the surface area), and a temperature of 18 °C. To calculate the power, we need to convert the temperature to Kelvin and use the formula.
First, let's convert the temperature to Kelvin:
TK = T + 273.15
Plugging in the values:
TK = 18 + 273.15
= 291.15 K
Now, we can calculate the power:
P = (0.35)(4πr2)(291.154)
where r is the radius of the sphere.
Plugging in the values:
P = (0.35)(4π(0.172))(291.154)
Using a calculator, we can compute the power to be approximately 182.44 watts.