Wallace and Hobbs 2.3 – The First Law of Thermodynamics

by Joe Archive on August 3, 2008

2.3 The First Law of Thermodynamicsbr /br /Internal energy of a body (or parcel of gas) – potential and kinetic energy of the constituent atoms: relative configurations and temperature respectively.br /br /consider a body that takes in a certain amount of heat energy q. The body may then do an amount of work, w, and be left with excess energy q-w. Conservation of energy implies that the internal energy, u, must increase by this amount:br /br /u2-u1 = q-wbr /br /or, for infinitesimal energy incrementsbr /br /du = dq-dwbr /br /2.3.1 Joule’s Lawbr /br /When a gas expands without either doing work or taking in (or loosing) heat, the temperature of the gas is constant (strictly only for an ideal gas, as inter-particle energies can change in real gasses, leading to a change in temperature to balance).br /br /2.3.2 Specific Heatsbr /br /c_v = dq/dT |_alphabr /c_p = dq/dT |_pbr /br /c_p = c_v + Rbr /dq = c_pdT -alpha dpbr /dq = c_vdT – p dalphabr /br /2.3.3 Enthalpybr /br /consider heat added to a material at constant pressure:br /br /dq = (u_2 – u_1) + p(alpha_2 – alpha_1) = (u_2+palpha_2) – (u_1 + palpha_1) = h_2 – h_1br /br /h == u + palpha br /br /h is the enthalpy per unit mass of the material.br /br /If the parcel is moving in a hydrostatic atmosphere:br /br /dq = d(h+Phi) br /br /so, h+Phi remains constant if the parcel moves adiabatically

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