Final answer:
To calculate the power consumption of a tungsten wire heating element at 150.0°C, the resistance at 80.0°C is first determined, and then this value is used to calculate the resistance at the higher temperature with the given temperature coefficient of resistivity. However, without the voltage or initial resistance values, a numerical solution for the power consumption at 150.0°C cannot be determined.
Step-by-step explanation:
The subject question involves calculating the power consumption of a tungsten wire heating element connected to a battery at two different temperatures, using the temperature coefficient of resistivity. The power consumed by the heating element at 80.0°C is given as 480 W, and we need to find its power consumption at 150.0°C, assuming a constant temperature coefficient of resistivity of 0.0045 (°C)^(-1) and a reference temperature of 20.0°C.
First, let's find the resistance of the heating element at 80.0°C (R80) using the formula P = V^2 / R, where P is the power. To find the resistance at 150.0°C (R150), we use the formula R150 = R80 * (1 + alpha * (T150 - Tref)), where alpha is the temperature coefficient of resistivity, T150 is the higher temperature of 150.0°C, and Tref is the reference temperature of 20.0°C.
Then, the power consumption at 150.0°C (P150) can be found using P150 = V^2 / R150, where V is the voltage across the heating element, which remains constant since the power supply has negligible internal resistance.
To perform these calculations accurately, the voltage at the initial condition needs to be known or calculated from the initial power and resistance; however, the voltage isn't provided in the question. Hence, we can't provide a numerical value for the power consumption at 150.0°C without additional information or assumptions.