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pressure and volume are inversely related. so at a constant volume, pressure is also constant. think about if you increase the pressure of a bike tire, the tire is also expanding and therefore there is a change in v, delta v. if delta v=0 then w=-pdeltav equals zero because the change in volume is zero. Therefore in the u=q+w equation, u equals q.
q represents the heat supplied to a system. Delta H represents the change in enthalpy, which is the change in energy as expansion work during heat transfer. When the pressure is constant, the heat supplied to a system is equal to the change in energy, so delta H and q are equal.
Also, enthalpy is specifically defined as the amount of heat absorbed or released under conditions of constant pressure. q represents heat absorbed/released, so qsubp is the same thing as enthalpy. qsubv is NOT the same thing as enthalpy.
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