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qv actually equals delta U. Since deltaU = q + work or deltaU = q - PdeltaV. Since qv means that there is a constant volume, then deltaV = 0 and work = 0, leaving deltaU = qv. On the other hand, qp=delta H because enthalpy (H) is defined as the amount of heat released/absorbed at a constant pressure. Therefore, qp, being heat at a constant pressure, equals delta H.
qv can not equal delta H because qv is constant volume, but the pressure of the system changes as the temperature increases(more random motion by gas particles), and the definition of enthalpy states that enthalpy is the amount of heat absorbed or released at constant pressure, so since the pressure of the system changes, qv can not equal delta H.
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