# Heat involved in isenthalpic process

Question 28 from [1, p. 4.4]:

An ideal gas is expanded irreversibly from $$\pu{5 L}$$ to $$\pu{10 L}$$ against a constant external pressure of $$\pu{1 bar}.$$ The value of heat involved $$(q)$$ in this isenthalpic process is

(a) $$0$$
(b) $$\pu{+500 J}$$
(c) $$\pu{+5 J}$$
(d) $$\pu{-500 J}$$

It is mentioned in the problem that the process is isenthalpic, which means the change in enthalpy must be zero. So, my conclusion was there is no heat involved here. But the answer given is (b).

### References

1. Neeraj, K. Advanced Problem in Physical Chemistry for Competitive Examinations, 2nd ed.; Pearson India Education Services Pvt. Ltd: Dehli, Chennai, 2015. ISBN 978-93-325-4373-7.

Isenthalpic processes on an ideal gas follow isotherms, since $$\mathrm dh = 0 = c_p\,\mathrm dT$$.
That means that for an ideal gas isenthalpic is synonymous with isothermal, and this implies $$\Delta U = 0$$ and so $$q = -w = P_\mathrm{ext}\Delta V$$.
For the isobaric process described in the problem, the work done by the gas is $$\pu{500 J}$$, and therefore the heat expected for an isothermal process is also $$\pu{500 J}$$.
* The source of my error is simple: for an irreversible process the heat is not equal to $$\Delta H$$. In fact, since the external pressure is not balanced by that of the system, $$P_\mathrm{ini}\neq P_\mathrm{fin}$$ for the system (the process is not strictly isobaric for the system). For a reversible isobaric process $$q_p = \Delta H$$.