1. Write down the equation used to account for the variation of molar heat capacity of a material at constant pressure with temperature assuming that the temperature range is significant.
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Step 1: The equation used to account for the variation of molar heat capacity of a material at constant pressure with temperature is the Kirchhoff's law. Show more…
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The Shomate equation for the constant pressure heat capacity of a substance is given by Cp = A + Bt + Ct^2 + Dt^3 + Et^-2, where t = T/1000, being the temperature in degrees Kelvin, and the heat capacity is in units of J/(K mol). The constants A, B, C, D, and E have specific values for a given compound and particular temperature range. We already saw in class that the molar enthalpy change associated with a constant pressure temperature change for the substance is worked out to be ΔH = A(t2 - t1) + B(t2^2 - t1^2) + C(t2^3 - t1^3) + D(1/t2 - 1/t1) + E(ln(t2/t1)). The enthalpy change in this equation is given in units of kJ/mol. Starting with the Shomate equation for the constant pressure heat capacity, we can work out the expression for ΔS for the constant pressure heating/cooling of the substance.
Sri K.
Using: • the algebraic expression of heat capacity,? =?/Δ? • the 1st Law of Thermodynamics, Δ? = ? + ?, and • the Ideal Gas Law, ?? = ???, to find a symbolic expression for ?? in terms of ?? and other constants. Recall ?? =Δ??ℎ/Δ? You should get: Cp = Cv + nR. 2) Using 1) solve for molar specific heat at constant pressure for a monatomic gas and compare to your result in 3)
Timothy J.
The approximate empirical expression for variation of molar heat capacity at constant pressure Cp,m with temperature is given by Cp,m = a + bT + c/T^2 [1] Calculate the change in molar enthalpy ΔHm when the given gas is heated from 25 °C to 500 °C using the expression above. The constants a, b, and c are available in Table 2B.1. [2] Evaluate Cp,m at 298 K using the above expression. What is ΔHm using this constant value of Cp,m? [3] Compare ΔHm from (1) and (2) and comment.
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