Calculate the amount of heat transferred through a steel plate given its dimensions, temperatures, and…

Question

Calculate the amount of heat transferred through a steel plate given its dimensions, temperatures, and thermal conductivity.

ScanSolve AI Tutor · Accepted Answer

To calculate the amount of heat flow, we use the formula for heat conduction:

Q = \frac{k \cdot A \cdot \Delta T \cdot t}{L}

where:
$Q$ = amount of heat transferred (Joules)
$k$ = thermal conductivity (K-value)
$A$ = cross-sectional area
$\Delta T$ = temperature difference
$t$ = time
$L$ = thickness

Identify the given values and convert them to SI units.
- Thickness, $L = 10 \text{ mm} = 0.01 \text{ m}$
- Width, $W = 0.6 \text{ m}$
- Length, $H = 1 \text{ m}$
- Time, $t = 30 \text{ minutes} = 30 \times 60 \text{ s} = 1800 \text{ s}$
- Temperature on one side, $T_1 = 70^\circ\text{C}$
- Temperature on the other side, $T_2 = 30^\circ\text{C}$
- K-value of steel, $k = 243 \text{ W/(m}\cdot\text{K)}$
Calculate the cross-sectional area ( $A$ ).
The heat flows through the area perpendicular to the thickness.
$A = W \times H$ $A = 0.6 \text{ m} \times 1 \text{ m}$ $A = 0.6 \text{ m}^2$
Calculate the temperature difference ( $\Delta T$ ).
$\Delta T = T_1 - T_2$ $\Delta T = 70^\circ\text{C} - 30^\circ\text{C}$ $\Delta T = 40^\circ\text{C}$
Since a change of $1^\circ\text{C}$ is equal to a change of $1\text{ K}$ , $\Delta T = 40\text{ K}$ .
Substitute the values into the heat transfer formula.
$Q = \frac{243 \text{ W/(m}\cdot\text{K)} \times 0.6 \text{ m}^2 \times 40 \text{ K} \times 1800 \text{ s}}{0.01 \text{ m}}$ $Q = \frac{10497600 \text{ J}}{0.01}$ $Q = 1049760000 \text{ J}$
The amount of heat that will flow through the sheet of steel is $\boxed{\text{1,049,760,000 J}}$ .

Calculate the amount of heat transferred through a steel plate given its dimensions, temperatures, and thermal conductivity.

Answer

Step-by-step solution

Identify the given values and convert them to SI units.

Calculate the cross-sectional area ( $A$ ).

Calculate the temperature difference ( $\Delta T$ ).

Substitute the values into the heat transfer formula.

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More Physics Questions

Calculate the amount of heat transferred through a steel plate given its dimensions, temperatures, and thermal conductivity.

Answer

Step-by-step solution

Identify the given values and convert them to SI units.

Calculate the cross-sectional area (AAA).

Calculate the temperature difference (ΔT\Delta TΔT).

Substitute the values into the heat transfer formula.

Try one yourself

Still stuck on this one?

More Physics Questions

Calculate the cross-sectional area ( $A$ ).

Calculate the temperature difference ( $\Delta T$ ).