a. 1 kg of liquid methanol (CH ₄ O) is compressed isothermally from 20°C and 1 bar to a final pressure of 1000 bar. Calculate the change in its entropy. Average density and volume expansivity (β) of liquid methanol at 20°C and over this pressure range are 0.80 g/cm ³ and 1.49 X 10 ^-3 oC ^-1

b. The Clausius equation of state is P (V- b) = R T, 

where b is a constant

Find an expression for the difference (C _p - C _v ) for a gas obeying this equation of state.