# Ideal Gas Law, P,T,V Change => adiabatic?

Given the expansion of an ideal gas, Pressure $P$, Volume $V$ and Temperature $T$ change from $P_1$, $V_1$, $T_1$, to $P_2$, $V_2$, $T_2$.

a) Does the standard ideal gas law predict correct end volume if all other variables are given. (Given $P_1$, $V_1$, $T_1$, to $P_2$, $T_2$)

b) Is this expansion of the ideal gas an adiabatic change? ($P$,$T$,$V$ change)

c) If not: How does one define the change in internal energy and enthalpy for an ideal gas with changes in all state variables, when it is not adiabatic?

a) If it is ideal gas, yes ideal gas will predict correct volume.

c) change in internal energy and enthalpy is only dependent on change in T.

(1) P, V, and T are state functions and do not depend on the thermodynamic path. Check the discussion here:

http://www.grandinetti.org/Teaching/Chem121/Lectures/Thermodynamics

(2) Not necessarily, it's adiabatic only if there is no heat transfer during the process.

(3) for a monoatomic ideal gas the internal energy is simply $\frac{3}{2} k_B T$ per ideal gas molecule or $\frac{3}{2} R T$ per mole of ideal gas.

Read up on the kinetic theory of gases and the equipartition of energy theorem. See page 26 onward here

http://www.grandinetti.org/resources/Teaching/Chem1910H/Chem1910H-1.pdf