Francia just relax its a hypothetical question just think the internal energy of the system changes because given heat to the system changes 

When a hemical reaction occurs in an open container most of the energy gained or lost is in the form of heat Almost no work is done Heat flows between the system and surroundings until the two are at the same temperature  
Under conditions of constant pressure (e.g. most biological processes under constant atmospheric pressure) the heat absorbed or released is termed enthalpy or heat contained   We do not measure enthalpy directly, rather we are concerned about the heat added or lost by the system, which is the change in enthalpy thats why the term enthalpy created :-) 
heat capacity at constant temperature defines dh/dt because
Internal energy = heat + work
dU = dq + dw integrate both side
DU= q+w
n many situations the potential energy and the kinetic energy of the system are constant.Then De = Du, andDu = q - w or DU = Q - WQ and W are path dependent, U is not it depends only on the state of the system, not how the system got to that state.dU = dQ - dW or du = dq - dw in this form u get its differential equation 
dU = dQ - dW (for any process, neglecting DKE and DPE)dU = dQ - pdV (for any quasi-static process, no DKE or DPE)H = U + pV therefore dH = dU + pdV + Vdpso dH = dQ - dW + pdV + Vdp (any process)ordH = dQ + Vdp (for any quasi-static process) thats why dh/dt is properly reduces to zero but not du/dt we cant take du/dt because its not reduces to zero i think u get it 

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