From K. Huang's Statistical Mechanics, par. 2.2:
Suppose a droplet of liquid is placed in an external medium that exerts a pressure $P$ on the droplet. Then the work done by the droplet on expansion is empirically given by
$$dW=P dV - \sigma da$$
where $da$ is the increase in the surface area of the droplet and $\sigma$ the coefficient of surface tension. The first law now takes the form
$$dU = dQ - P dV + \sigma da$$
Integrating this, we obtain for the internal energy of a droplet of radius $r$ the expression
$$U = \frac 4 3 \pi r^3 u_\infty + 4 \pi \sigma r^2$$
where $u_\infty$ is the internal energy per unit volume of an infinite droplet.
I don't understand this last passage.
I do understand the second term, since
$$\sigma \int da = 4 \pi \sigma r^2$$
but frankly I don't understand where the first term is coming from. Why should
$$\int dQ - \int P dV = \frac 4 3 \pi r^3 u_\infty$$