What is the difference in the two notation?

Question

I have read in Zeemansky's physics

$dQ=dU+pdV$ for first law of thermodynamics

But when I came across another book of thermal physics,it says

$δQ= dU +pdV$. So what us the difference ?

Answer 1

The notation $\delta Q$ is sometimes used to denote the fact that there may not be a well defined function $Q$. It simply means "small increment". It is used to underlie the distinction between say the energy $U=U(p,V)$, which is a function of state and stuff like $Q$ and $W$, which are not functions of state. So for example I can write: $$dU = \frac{\partial U}{\partial p}dp+\frac{\partial U}{\partial V}dV$$ You can't do this with $Q$, say, because it's not a function of state.

If one wants to be more mathematically precise, both are mathematical objects called differential forms. Only $dU$ is an exact form, $\delta Q$ is not.

Answer 2

For heat, the difference is purely notational. In both cases, infinitesimal heat transfer is being modeled as a differential form -- the authors are simply using different notations for that same differential form.

Often authors rightly prefer to use "$\delta$" to indicate that heat is an inexact differential form so the "$d$" can be reserved for exact forms which, by definition, can be written as the differential (aka exterior derivative) of another form. See, for example, closed and exact differential forms