(a) What are meant by reduced temperature and reduced pressure?

(b) Prove that van der Waals constants \((a, b)\) can be expressed in terms of critical temperature and pressure as follows:
$$a=\frac{27R^2{T}_c^2}{64P_c}b=\frac{R{T}_c}{8P_c}$$

(c) $1mol$ of an ideal gas is reversibly and adiabatically compressed from an initial volume of $30\times {10}^{-3}{m}^3$ to a final volume of $10\times {10}^{-3}{m}^3$. The initial temperature of the gas is $300K$. What are the final pressure and temperature? Calculate the work done. $C_V$ of the gas is $\frac{5}{2}R$.