For a perfect gas, the internal energy ([latex]U[/latex]) and enthalpy ([latex]H[/latex]) are functions of temperature only. Their changes are given by [latex]\Delta U = m c_v \Delta T[/latex] and [latex]\Delta H = m c_p \Delta T[/latex], where [latex]c_v[/latex] and [latex]c_p[/latex] are the specific heats at constant volume and 压力, respectively, and are assumed to be constant.
A cornerstone of the perfect gas model is the principle that its internal energy depends solely on its temperature. This was experimentally demonstrated by James Prescott Joule in his expansion experiments. For an ideal gas, internal energy is the sum of the kinetic energies of its constituent molecules. Since temperature is a measure of the average kinetic energy, internal energy is a function of temperature. The perfect gas model simplifies this further by assuming a linear relationship through a constant specific heat at constant volume, [latex]c_v[/latex]. Thus, the change in specific internal energy is [latex]\Delta u = c_v \Delta T[/latex].
Enthalpy ([latex]H[/latex]) is a 热力学 potential defined as [latex]H = U + PV[/latex]. For a perfect gas, using the 理想气体定律 ([latex]PV = nRT[/latex]), enthalpy becomes [latex]H = U(T) + nRT[/latex], which is also a function of temperature only. The change in specific enthalpy is similarly given by [latex]\Delta h = c_p \Delta T[/latex], where [latex]c_p[/latex] is the constant specific heat at constant pressure. This simplification is immensely powerful in engineering, as it allows for straightforward calculation of energy changes in processes like compression, expansion, and heating without needing complex tables or equations of state, forming the basis for analyzing engines, refrigerators, and power plants.
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