There are a few models of the relationship between pressure, specific volume, and temperature for gases. These models are generally conceptualizes gas as a collection of particles all bouncing around, off of the walls of a container and off of one another.
The most generalize empirical model is the generalized compressibility model. A generalized compressibility chart gives the compressibility, $Z$, characteristic to a particular gas at a particular temperature and pressure.
The chart has a horizontal axis of relative pressure, the ratio of the gas’ current pressure to the pressure of its critical point, and curves for various values of relative temperature, the ratio of the gas’ current temperature to the temperature of its critical point. The vertical axis value of the appropriate relative temperature curve at the appropriate relative pressure gives the compressibility.
$$ p_{R}=\frac{p}{p_c}~~~~~T{_R}=\frac{T}{T_c} $$
This compressibility value is then used to relate pressure, specific volume, and temperature according to the following. Also included is the gas constant, $R=8.3145\frac J{mol\cdot K}$.
$$ Z=\frac{pv}{RT} $$
The tendency of compressibility to approach one for low relative pressures and high relative temperatures is what gives rise to the ideal gas model.
$$ pv=RT $$
Recall that we are modeling the gas as a collection of bouncing particles. The ideal gas model entails that the volume of these particles (atoms or molecules) is negligible with respect to the volume of their container, that there are no inter-particle forces, that the collisions are perfectly elastic, that is, conserving kinetic energy, and that the particles are thereby in continuous, random motion.
The ideal gas law, by relating pressure, specific volume, and temperature, entails that internal energy and enthalpy vary only with respect to temperature.
$$ u=u(T)~~~~~h=u+pv=u(T)+RT $$
As such, the change in internal energy for a constant volume process, or in enthalpy for a constant pressure process, may be found by integrating specific heat with respect to temperature. Given a table of specific heats, this integral can be approximated by summation.
$$ \Delta u=\int_{T_1}^{T_2}c_v(T)dT~~~~~~\Delta h=\int_{T_1}^{T_2}c_p(T)dT $$
Constant specific heat approximations give a further approximation of the integrals by a single product.