Question

The heat flux (from outside to inside) across an insulating wall with thermal conductivity, k= 0.04 W/(m K) and thickness 0.16m is 10 W/m2. The temperature of the inside wall is -5 °C. The outside wall temperature is

A. 30 C
B. 25 C
C. 35 C
D. 40 C

Answer 1

The heat flux (from outside to inside) across an insulating wall with thermal conductivity, k= 0.04 W/(m K) and thickness 0.16m is 10 W/m2. The temperature of the inside wall is -5 °C. The outside wall temperature is 35°C (option C).

Step-by-step explanation:

The temperature of the outside wall can be determined using the formula for heat flux (q):

`\[ q = (k \cdot \Delta T)/(d) \]`

where (k) is the thermal conductivity,
`\(\Delta T\)` is the temperature difference, and (d) is the thickness of the wall. Rearranging the formula to solve for the temperature difference:

`\[ \Delta T = (q \cdot d)/(k) \]`

Substitute the given values
`(\(q = 10 \, \text{W/m}^2\), \(d = 0.16 \, \text{m}\), \(k = 0.04 \, \text{W/(m K)}\)):`

`\[ \Delta T = (10 \cdot 0.16)/(0.04) \]`

`\[ \Delta T = 40 \, \text{K} \]`

Now, determine the outside wall temperature by adding the temperature difference to the inside wall temperature:

`\[ \text{Outside wall temperature} = \text{Inside wall temperature} + \Delta T \]`

`\[ \text{Outside wall temperature} = (-5) + 40 \]`

`\[ \text{Outside wall temperature} = 35 \, \text{°C} \]`

Therefore, the correct answer is C. 35°C.