Thermo Lab Experiment 1

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I. Objective

The first objective of the measurement of thermal conductivity & one-dimensional heat conduction experiment was to identify three different metal specimens by comparing their experimentally determined thermal conductivities to known thermal conductivity values of existing metals. The second objective of the experiment was to establish a connection between the thermal conductivities & temperatures of the metal specimens. Thirdly, the contact resistance of the interfaces between the specimens was to be determined.

II. Theory

Particles of a substance always interact with each other. There’s a transfer of energy with each of there interactions. The energy is transferred from the higher excited particles to the lesser excited particles, which this energy transfer is called conduction. Fourier’s Law governs conduction, which deems that the heat transferred through a substance is proportional to the change in temperature over the substances thickness. The ability to transfer heat through conduction is dependent on the substances thermal conductivity, which is denoted as k. The property k is dependent on the substances atomic structure & temperature, which will be verified in this experiment. The governing law of conduction, known as Fourier’s Law of Heat Conduction is represented by the equation: [4]

Qcond= -kAcdTdx
(1)

Qcond represents the rate of heat conduction; Ac represents the cross-sectional area that the heat is being transferred through; k represents the thermal conductivity of the material; dTdx represents the approximation for temperature gradient across the thickness of the substance.

Ac, which represents the cross-sectional area that the heat is being transferred through, can be calculated by using the following equation: [4]

Ac= π4D2
(2)

D represents the diameter of the specimen.

Conduction through solids occurs in all three directions, but in this experiment the heat is assumed to only conduct axially. The assumption of the heat only conducting axially is due to the cylindrical specimens being insulated radially. This doesn’t negate radial conduction completely, but it improves the accuracy of the experiments one-dimensional axial conduction analysis. According to the energy conservation theory, all of the heat added to the specimen must be transferred to the other end. Theoretically, the entirety of the heat transferred through the specimen will be transferred completely to the cooling water in the heat sink. The equation that represents this is: [4]

Qcond= mc(he-hi)c
(3)

mc represents the mass flow rate of the cooling water; he represents the specific enthalpy of the cooling water at the exit; hi represents the specific enthalpy of the cooling water at the inlet.

mc can be calculated by the following equation: [1]

mc=Vcρc
(4)

Vc represents the volumetric flow rate of the cold water; ρc represents the density of the cold water.

Vc can be calculated by measuring the amount of time it takes to fill a graduated cylinder a certain volume. The equation for calculating Vc is: [1]

Vc=ΔVΔt
(5)

ΔVΔt represents the change in volume over the change in time.

The thermal conductivity of the specimen can be calculated now by measuring the temperature gradient across the specimen. Verifying that the experiment is done under steady state conditions, the equation to calculate the temperature gradient is: [1]

dTdx=T2-T1x2-x1
(6)

Fourier’s Law of Heat Conduction found in equation 1 can be re-written & rearranged to solved for the thermal conductivity, substituting equation 6 in for dTdx: [1]

kexp= -QcondAcdTdx
(7)

Once the kexp is calculated for each specimen, then compare each specimen kexp value to existing known k values for the given possible metals the specimens could be. The equation to figure out the actual k values for the possible metals given for the specimen is: [2]

ktabulated=ko-aT-T0
(8)

ko & a...
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