The correct expression is: deltaE (Internal Energy) = delta q (change in heat) - PdeltaV (change in work). This expression is always valid, regardless of which convention you use for work (physics or chemistry). Because they expressed that relationship in terms of deltaH, then they must be refering to an instance where pressure is constant. In such a scenario, delta q = delta H and so you can substitute the expression as follows: deltaE = deltaH - PdeltaV.
Thank you. Your post is verified to be true by several sources online. My TPR biology book has a mistake in it.
However, be careful about the term PdeltaV. This expression is derived under the assumption that pressure is constant while volume is allowed to change. If volume is kept constant Delta E= Delta H=q because work no longer can be done by the system or done on the system
That's partially true, but I just want to clarify that the P term in PdeltaV is atmospheric pressure acting on a contained gas (such as that in a piston) - that is, the surroundings themself. However, when they refer to pressure being constant, they are referring to inside the gas container. But regardless, you're still right. If deltaV=0, implying no work is done, then that whole term is just zero and deltaE=deltaq (an isochoric process). I definitely wouldn't say though that deltaE=deltaH because in this particular scenario, the pressure is very likely to be changing (because the volume cannot expand or compress to compensate).
Yes you right. H=E+PV dH=dE+(dP)V under constant volume.
