In Chapter 4 of Chemical Thermodynamics, by Peter A. Rock published by Oxford University Press, 1983, the author is trying to explain why a new state function is needed, specifically a state function relating entropy. He starts off with an equation from the first law for an adiabatic, reversible expansion of an ideal gas.
$C_V\ln(\frac{T_2}{T_1}) + nR\ln(\frac{V_2}{V_1}) = 0$
He then goes onto explain the equation above by saying:
Equation (1) has an interesting consequence, namely, that given $T_1$ and $V_1$ we are free to pick $T_2$ or $V_2$ but not both; otherwise eq(1), which relates $T_1$, $V_1$ and $T_2$, $V_2$, would be violated.
I don't understand why picking two variables violates the equation.