A body of length `1 m` having cross sectional area `0.75 m^(2)` has heat flow through it at the rate of `6000 "Joule"//sec`. Then find the temperature difference if `K = 200 Jm^(-1) K^(-1)`.

Options

A. `20^(@)C`
B. `40^(@)C`
C. `80^(@)C`
D. `100^(@)C`

Explanation

To solve the problem, we will use the formula for heat conduction, which is given by Fourier's law:

\[ \frac{dq}{dt} = \frac{k \cdot A \cdot \Delta T}{L} \]

Where:
- \(\frac{dq}{dt}\) is the rate of heat flow (in Joules per second),
- \(k\) is the thermal conductivity (in \(J \cdot m^{-1} \cdot K^{-1}\)),
- \(A\) is the cross-sectional area (in \(m^2\)),
- \(\Delta T\) is the temperature difference (in Kelvin or Celsius),
- \(L\) is the length of the body (in meters).

Given:
- \(\frac{dq}{dt} = 6000 \, \text{J/s}\)
- \(k = 200 \, \text{J} \cdot m^{-1} \cdot K^{-1}\)
- \(A = 0.75 \, m^2\)
- \(L = 1 \, m\)

We need to find the temperature difference \(\Delta T\).

### Step 1: Rearranging the formula
We can rearrange the formula to solve for \(\Delta T\):

\[ \Delta T = \frac{\frac{dq}{dt} \cdot L}{k \cdot A} \]

### Step 2: Substituting the values
Now, we substitute the known values into the equation:

\[ \Delta T = \frac{6000 \, \text{J/s} \cdot 1 \, \text{m}}{200 \, \text{J} \cdot m^{-1} \cdot K^{-1} \cdot 0.75 \, m^2} \]

### Step 3: Calculating the denominator
Calculating the denominator:

\[ 200 \cdot 0.75 = 150 \, \text{J} \cdot K^{-1} \]

### Step 4: Completing the calculation
Now substituting back into the equation:

\[ \Delta T = \frac{6000}{150} \]

Calculating this gives:

\[ \Delta T = 40 \, K \]

### Conclusion
The temperature difference \(\Delta T\) is \(40 \, K\) or \(40 \, °C\).