The U.S. five-cent coin, the nickel, has a mass of 5.1 g, a volume of 0.719 cm3, and a total surface area of 8.54 cm2. Assuming that a nickel is an ideal radiator, how much radiant energy per second comes from the nickel, if it is at 24∘C?
use the equation P = AoT^4
where P is Q/t
A is surface area
"o" is actually the greek letter for Stefan Boltzman constant :
5.67x10^(-8) J/s*m^2*K^4
* not greek letters on keyboard lol
and T is temperature in kelvin
DON'T FORGET TO CONVERT YOUR UNITS
You should get:
P= A o T^4
P = (8.54x10^(-4))(5.67x10^(-8))(24+273)^4
A is 8.54x10^(-4) because you have to convert cm^2 to m^2 because of the units for Boltzman's constant
To calculate the amount of radiant energy per second emitted by the nickel, we can use the Stefan-Boltzmann law, which states that the power radiated by an object is directly proportional to its surface area and its temperature raised to the fourth power.
The equation for the power radiated by an object is given by:
P = σ * A * T^4
Where:
P is the power radiated (measured in watts),
σ (sigma) is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4),
A is the surface area of the nickel (measured in square meters), and
T is the temperature of the nickel (measured in Kelvin).
To calculate the surface area and temperature in the appropriate units, we need to convert the given values:
- The mass is not necessary for this calculation.
1. Convert the volume from cm^3 to m^3:
0.719 cm^3 = 0.719 x 10^-6 m^3 (1 cm^3 = 10^-6 m^3)
2. Convert the surface area from cm^2 to m^2:
8.54 cm^2 = 8.54 x 10^-4 m^2 (1 cm^2 = 10^-4 m^2)
3. Convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T = 24 + 273.15 = 297.15 K
Now, we can plug in the converted values into the equation and solve for power (P):
P = σ * A * T^4
P = (5.67 x 10^-8 W/m^2K^4) * (8.54 x 10^-4 m^2) * (297.15 K)^4
Calculating the expression:
P = 0.0056637 W
Therefore, the nickel emits approximately 0.0056637 watts of radiant energy per second when it is at a temperature of 24°C.
To calculate the radiant energy per second (also known as radiant power) emitted by the nickel, we can use the Stefan-Boltzmann Law, which states that the power radiated by an ideal radiator is proportional to the fourth power of its temperature. The formula is:
P = σ * A * ε * T^4
Where:
P = radiant power (in watts, W)
σ = Stefan-Boltzmann constant (5.67 x 10^-8 W/(m^2⋅K^4))
A = surface area of the nickel (in square meters, m^2)
ε = emissivity of the nickel (assumed to be 1 for an ideal radiator)
T = temperature of the nickel (in Kelvin, K)
First, we need to convert the given values to the appropriate units:
Mass of the nickel = 5.1 g
Volume of the nickel = 0.719 cm^3
Total surface area of the nickel = 8.54 cm^2
Temperature of the nickel = 24°C
The mass and volume of the nickel are not directly needed for this calculation but are given for informational purposes.
To find the surface area in square meters, we need to convert cm^2 to m^2:
Surface area of the nickel = 8.54 cm^2 * (0.01 m / 1 cm)^2 = 0.854 m^2
Now, we need to convert the temperature from Celsius to Kelvin:
Temperature of the nickel in Kelvin = 24°C + 273.15 = 297.15 K
Now that we have all the required values, we can calculate the radiant power:
P = σ * A * ε * T^4
= (5.67 x 10^-8 W/(m^2⋅K^4)) * 0.854 m^2 * 1 * (297.15 K)^4
Calculating the equation will give you the radiant power emitted by the nickel in watts (W).