Question

Some stove tops are smooth ceramic for easy cleaning. If the ceramic is 0.600 cm thick and heat conduction occurs through a 14 cm radius and at a rate of 2256 W, what is the temperature difference across it? Ceramic has the same thermal conductivity as glass and brick.

(a) 100°C
(b) 150°C
(c) 200°C
(d) 250°C

Answer 1

The temperature difference across the ceramic stove top is approximately 99.3°C.

Step-by-step explanation:

To find the temperature difference across the ceramic stove top, we can use the formula:

Q = (k * A * ΔT) / d

Where Q is the rate of heat conduction, k is the thermal conductivity, A is the area, ΔT is the temperature difference, and d is the thickness of the ceramic.

Using the given information, we can rearrange the formula to solve for ΔT:

ΔT = (Q * d) / (k * A)

Plugging in the values:

ΔT = (2256 W * 0.600 cm) / (k * π * (14 cm)^2)

Since ceramic has the same thermal conductivity as glass and brick, we can use the thermal conductivity of glass (1.05 W/(m·K)). Solving the equation gives us:

ΔT = 99.3°C

Therefore, the temperature difference across the ceramic stove top is approximately 99.3°C.