For specific
heat measurements, the sample is in the "long" rod configuration so
that dT/dZ=d^2T/dZ^2 = 0 over the central portion of the rod. That
section of the sample between the voltage probes is used in the
calculations and the mass (m) of this portion of the sample is
calculated from the density, cross-sectional area (A), and distance
between the voltage probes (L). For the case of this central
portion of a long rod directly heated in vacuum but not at steady
state, Eq (10) becomes
If we impose a step function change in the current flow from an
equilibrium current, we can obtain the expression
where Ie and Ve are the equilibrium current and voltage at T,
I and V are current and voltage when the transient temperature is
T, and dT/dt is the rate of change of temperature at T. The
rate of temperature change is controlled by the difference between
IV and Ie Ve .
The rate of temperature change can be measured directly using automatic optical pyrometry or thermocouples or determined indirectly from the electrical resistivity. The use of the electrical resistivity is preferred when the temperature coefficient of the resistivity is fairly large. Transient temperature measurements using thermocouples requires some expertise, particularly when measuring temperature of samples which are directly heated by DC current (due to substantial offset problems).
If the electrical resistivity is to be used as the temperature detector, the electrical resistivity is first determined as a function of true temperature. This is accomplished by placing the auxiliary tantalum tube furnace and heat shields around the sample. At the lower temperatures, thermocouples are used to measure the sample temperature, and at higher temperatures, optical pyrometry is used. The hole in the heater and heat shields is aligned with the optical window so that the sample can be viewed through the hole. Power is applied to both the heater and sample so that their temperatures are maintained nearly equal (in the pyrometer range). This is accomplished by independently varying the power supplied to both the sample and heater until the sample's edge blends into the back wall of the heater. Under these conditions the effective emissivity is 1.00 and the brightness temperature is the true temperature. Voltage, current and temperature measurements are made, the current flow in the sample is reversed and the measurements repeated and averaged. The electrical resistivity is calculated using Eq. (6). This procedure is repeated until sufficient data are determined to define the resistivity(T) curve. Following the resistivity(T) determination, the sample is heated to a preselected temperature and voltage and current data are obtained at selected temperatures. After this equilibrium data has been obtained transient data is taken. From these V (time) and I (time) data,a the specific heat is calculated using computer programs and Eq. (11).
If the transient temperature is to be measured directly using an automatic pyrometer, a calibration run is made. No external furnace is required. The long sample is heated to the temperature of interest and the voltage, current, brightness temperature, and transient temperature (voltage reading directly from photomultiplier tube) are measured. The sample temperature is changed slightly and the readings are repeated. This procedure is repeated until the temperature range to be measured (usually about 150 C) is covered. Then the sample temperature is adjusted to a point near the top or bottom of this temperature range, and voltage, current, and transient temperatures as a function of time are recorded while the current level is changed in a step-wise fashion to cover about the same temperature range that the calibration run was made. The specific heat values area computed from these data using a computer program and Eq. (11).
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