# 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?

## 2 Answers

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

b) You can expand an ideal gas adiabatically and non-adiabatically.

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