A rod of length 1 having cross sectional area 0.75 m square conducts heat of 6000J/S. Then the temperature difference across the rod is if K=200 wm^-1K^-1

To find the temperature difference across the rod, we can use Fourier's law of heat conduction, which states that the rate of heat transfer (Q) through a material is proportional to the temperature difference (ΔT) across it, the area (A) through which the heat is conducted, and inversely proportional to the length (L) of the material. The formula can be expressed as:

Fourier's Law of Heat Conduction

The formula is given by:

Q = k * A * (ΔT / L)

Where:

• Q = rate of heat transfer (in watts or joules per second)
• k = thermal conductivity of the material (in W/m·K)
• A = cross-sectional area (in m²)
• ΔT = temperature difference across the material (in K or °C)
• L = length of the material (in m)

Given Values

From your question, we have the following values:

• Q = 6000 J/s
• A = 0.75 m²
• L = 1 m
• k = 200 W/m·K

Rearranging the Formula

To find the temperature difference (ΔT), we can rearrange the formula:

ΔT = (Q * L) / (k * A)

Substituting the Values

Now, we can substitute the known values into the rearranged formula:

ΔT = (6000 J/s * 1 m) / (200 W/m·K * 0.75 m²)

Calculating the Temperature Difference

Let's perform the calculation step by step:

• First, calculate the denominator: 200 W/m·K * 0.75 m² = 150 W/K
• Now, substitute this back into the equation: ΔT = 6000 J/s / 150 W/K
• Finally, calculate ΔT: ΔT = 40 K

Final Result

The temperature difference across the rod is 40 K. This means that there is a significant temperature gradient along the length of the rod, which is essential for efficient heat conduction.