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A student is trying to determine the heat capacity of a substance at constant pressure, given its thermodynamic properties. The substance is in the gas phase and is confined to a container at a specific temperature and pressure. What is the mathematical expression for the heat capacity of the substance in terms of its thermodynamic properties, and what is the numerical value of the heat

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The heat capacity of a substance at constant pressure  Cp  can be determined using its thermodynamic properties. For an ideal gas, the heat capacity at constant pressure can be expressed in terms of its molar heat capacity  Cp,m  and the number of moles  n  of the substance:Cp = n * Cp,mThe molar heat capacity at constant pressure  Cp,m  depends on the specific gas and its temperature. For many gases, Cp,m can be approximated using the following empirical equation:Cp,m = a + bT + cT^2 + dT^3where T is the temperature in Kelvin, and a, b, c, and d are constants specific to the gas. These constants can be found in thermodynamic tables or literature.To determine the numerical value of the heat capacity at the given temperature and pressure, you would need to know the number of moles  n  of the substance, the temperature  T , and the constants  a, b, c, and d  for the specific gas. Then, you can calculate Cp,m using the empirical equation and multiply it by the number of moles  n  to find the heat capacity  Cp .The heat capacity of a substance can change with temperature or pressure. For an ideal gas, the pressure does not significantly affect the heat capacity. However, the temperature does have an effect on the heat capacity, as seen in the empirical equation for Cp,m. As the temperature increases or decreases, the heat capacity will change accordingly due to the temperature-dependent terms in the equation.

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