The Kelvin temperature of an object is T1 and the object radiates a certain amount of energy per second. The Kelvin temperature of the object is then increased to T2, and the object radiates 81 times as much energy per second as it radiated at the lower temperature. What is the ratio T2/T1?
To find the ratio T2/T1, we need to set up an equation using the given information.
Let's assume that the amount of energy radiated by the object at temperature T1 is E1, and the amount of energy radiated by the object at temperature T2 is E2.
According to the problem, when the temperature is increased from T1 to T2, the object radiates 81 times as much energy per second. In other words, we can write the equation:
E2 = 81 * E1
We also know that the energy radiated by an object is proportional to the fourth power of its temperature (as described by the Stefan-Boltzmann law). Mathematically, we can express this relationship as:
E2/E1 = (T2^4) / (T1^4)
Substituting the value of E2 from the earlier equation, we get:
81 * E1 / E1 = (T2^4) / (T1^4)
Simplifying the equation, we find:
81 = (T2^4) / (T1^4)
To find the ratio T2/T1, we can take the fourth root of both sides of the equation:
∛(81) = ∛((T2^4) / (T1^4))
Simplifying further, we get:
3 = (T2 / T1)
Therefore, the ratio T2/T1 is 3.
Let's assume that the amount of energy radiated by the object is directly proportional to the fourth power of its Kelvin temperature. This assumption is based on Stefan-Boltzmann's law, which states that the energy radiated by an object is proportional to its surface area and the fourth power of its Kelvin temperature.
Let's denote the initial amount of energy radiated at temperature T1 as E1, and the increased amount of energy radiated at temperature T2 as E2.
According to the given information, we have the following relationship:
E2 = 81 * E1
Using the proportional relationship, we can write the following equation:
(T2^4) = 81 * (T1^4)
Taking the fourth root of both sides of the equation, we get:
T2 = (81^(1/4)) * T1
Simplifying the right-hand side of the equation, we have:
T2 = 3 * T1
Therefore, the ratio T2/T1 is 3.
energy is proportional to temp to the forth power.
fourth root of 81
3^4=81