# Solve for Cold Surface Temp. of Slab with Heat Flow Rate 240 W

• yankees26an
In summary, the heat flow rate through a 0.83 m2 slab with a thickness of 1.4 cm and a thermal conductivity of 0.6 W/(m·K) is 240 W. Using the equation ΔQ/Δt=-kA(Δθ/Δt), the temperature difference between the hot surface at 40°C and the cold surface can be calculated to be 578 K. This is significantly higher than all given answer options, indicating a potential error in the calculations.
yankees26an

## Homework Statement

The absolute value of the heat flow rate through a slab of area 0.83 m2 is 240 W. The
thickness of the slab is 1.4 cm and its thermal conductivity is 0.6 W/(m·K). If the hot surface of the slab is at 40°C find the temperature of the cold surface.

## Homework Equations

H = -kA($$\Delta$$T/$$\Delta$$x)

H = Q/t?

## The Attempt at a Solution

A = 0.83 m^2; $$\Delta$$x = 1.4; k = 0.6 W/(m·K); Thot = 40°C;

Missing H?

yankees26an said:

## Homework Equations

H = -kA($$\Delta$$T/$$\Delta$$x)

H = Q/t?

this should be

$$\frac{dQ}{dt}=-kA \frac{d\theta}{dx}$$

or

ΔQ/Δt=-kA(Δθ/Δt)

you were given ΔQ/Δt as 240 W

ok so

$$\Delta$$T = ($$\Delta$$x*H)/(kA)

$$\Delta$$T = 1.2*240/0.6*0.83

$$\Delta$$T = 578 K = 305 C ?? That's way above any answer options

yankees26an said:
$$\Delta$$T = 1.2*240/0.6*0.83

this should be 0.014m

## 1. What is the formula for calculating the cold surface temperature of a slab with a heat flow rate of 240 W?

The formula for calculating the cold surface temperature of a slab with a heat flow rate of 240 W is: Tc = Th - (Q/Ak), where Tc is the cold surface temperature, Th is the hot surface temperature, Q is the heat flow rate, A is the cross-sectional area of the slab, and k is the thermal conductivity of the slab.

## 2. How do I determine the hot surface temperature in the formula for calculating the cold surface temperature?

The hot surface temperature can be determined by measuring the temperature at the surface of the slab where heat is being applied. This can be done using a thermometer or temperature sensor.

## 3. What units should be used for the heat flow rate and thermal conductivity in the formula?

The heat flow rate should be measured in watts (W), while the thermal conductivity should be measured in watts per meter per Kelvin (W/mK).

## 4. Can this formula be used for any type of slab?

This formula is most commonly used for homogeneous slabs, meaning the material and thickness are consistent throughout. It may not be accurate for slabs with varying materials or thicknesses.

## 5. How accurate is this formula in determining the cold surface temperature?

The accuracy of this formula depends on the accuracy of the measurements used and the assumptions made about the slab, such as its homogeneity. It is always best to double check the results with other methods or consult a professional if precision is crucial.

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