Seeking Appropriate Equation for Linear Conductivity

[enter8]

Homework Statement

I am attempting to calculate the approximate time it takes for a stone slab to fully preheat, focusing only on one dimensional steady flow conduction. Both my area and mass are unknown.

Thermal conductivity: 6.4 W/mK
Specific heat capacity: 0.98 J/gK
Density: 2,980 kg/m³

Thickness of slab: 3.18 cm
Distance to center: 1.59 cm
T1: 260 C.
T2 (core): 21.11 C.

Homework Equations

This is what I'm looking for.

The Attempt at a Solution

I've spent hours looking through textbooks trying to find the right equation, but everything I run across seems to have additional info such as area and mass.

 

[Andrew Mason]

You will have to give us the whole problem. Area and mass are needed but I suspect that they fall out in your calculation.

AM

 

[kerimek]

Can anyone please help

As a scientist, it is important to use the appropriate equation for any given problem. In this case, the equation you are looking for is the one-dimensional steady-state heat conduction equation:

Q = kA(T2-T1)/L

Where Q is the heat flow rate, k is the thermal conductivity, A is the cross-sectional area, T1 and T2 are the temperatures at the two ends of the slab, and L is the thickness of the slab.

Since you do not have the area and mass information, you can use the density and thickness to calculate the cross-sectional area A = m/(ρL), where m is the mass of the slab and ρ is the density. Then, plug in the values you have for k, T1, T2, and A into the equation to solve for Q. From there, you can calculate the time it takes for the slab to fully preheat using the heat capacity equation:

Q = mcΔT

Where Q is the heat flow rate, m is the mass of the slab, c is the specific heat capacity, and ΔT is the change in temperature. You can rearrange this equation to solve for time, t = Q/(mcΔT). This will give you the approximate time it takes for the slab to fully preheat.