To calculate the average temperature of the rod, we need to integrate the temperature function over the entire length of the rod and divide by the length. Using the given information, the average temperature is (1/3) * (3T0 + 75) degrees Celsius, where T0 represents the temperature at one end of the rod.
To calculate the average temperature of the rod, we need to understand the temperature variation along the length of the rod. The given information states that the temperature of the rod is a function of the distance from one end, denoted by x.
Since the rod is 3 meters long, we can assume that x ranges from 0 to 3 meters. At one end of the rod (x = 0), the temperature is not specified, so we'll denote it as T0.
At the other end of the rod (x = 3 meters), the temperature is given as 25x degrees Celsius. Substituting x = 3 into the equation, we find that the temperature at the end of the rod is 25 * 3 = 75 degrees Celsius.
To calculate the average temperature, we need to integrate the temperature function over the entire length of the rod and then divide by the length. Using the given information, the integral becomes:
Average temperature = (1/3) * ∫(T0 + 25x) dx from 0 to 3
Integrating, we get:
Average temperature = (1/3) * [T0x + (25/2)x^2] evaluated from 0 to 3
Simplifying further, we have:
Average temperature = (1/3) * (3T0 + 75)
So, the average temperature of the rod is given by (1/3) * (3T0 + 75) degrees Celsius.