The power of the heater is 750 W750 W at 1000∘ C1000° C. What will be its power at 200∘ C200° C if thermal coefficient of resistance is α=4×10−4 °C−1𝛼=4×10-4 °C-1?

The power of a heater is given by the formula P = V^2 / R, where V is the voltage and R is the resistance.

The resistance of a heater at a certain temperature can be calculated using the formula R = R0 * (1 + α * ΔT), where R0 is the resistance at a reference temperature (usually 20°C), α is the temperature coefficient of resistance, and ΔT is the change in temperature from the reference temperature.

Given that the power of the heater is 750W at 1000°C, we can calculate the resistance at this temperature. Let's assume that the voltage is constant, so we can write the power as P = V^2 / R. Solving for R gives us R = V^2 / P.

We don't know the exact value of V, but we know that it's constant, so we can say that the resistance at 1000°C (R1000) is proportional to 1/P, or R1000 = k / P, where k is a constant.

Now, we want to find the power at 200°C. We can use the formula for resistance at a certain temperature to find the resistance at 200°C (R200).

R200 = R0 * (1 + α * ΔT) = R1000 * (1 + α * (200 - 1000)) = R1000 * (1 - α * 800).

Substituting R1000 = k / P into this equation gives us R200 = k / P * (1 - α * 800).

Finally, we can find the power at 200°C (P200) by substituting R200 into the power formula:

P200 = V^2 / R200 = V^2 / (k / P * (1 - α * 800)) = P / (1 - α * 800).

Given that α = 4 * 10^-4 °C^-1, we can substitute this into the equation to find P200:

P200 = 750W / (1 - 4 * 10^-4 * 800) = 750W / (1 - 0.32) = 750W / 0.68 ≈ 1103W.

So, the power of the heater at 200°C is approximately 1103W.