Question 1: 

Heat capacities C_v and C_p are defined as temperature derivatives respectively of U and H. Show that the general expression connecting C_p to C_v is:

 Question 2

Liquid isobutane is throttled through a valvefrom an initial state of 360 K and 4000 kPa to a final pressure of 2000 kPa. Estimate the entropy change of the isobutane. The specific heat of liquid isobutane at 360 K is 2.78 J/g/°C.

For volume calculation, use equation:

 Given: V_c= 262.7 cm³/mol, Z_c= 0.282 and T_c= 408.1 K

Also, change in T and V is negligible during throttling process.

Question 3

A concentrated binary solution containing mostly species 2 (but x₂ not equals to 1) is in equilibrium with a vapor phase containing both species 1 and 2. The pressure of this two-phase system is 1 bar; and the temperature is 25°C. Determine from the following data good estimates of x₁ and y₁.

Given: H₁ = 200 bar,    P₂^sat = 0.1 bar

State and justify all assumptions.

Question 4 

For the acetone(1)/methanol(2) system a vapor mixture for which z₁ = 0.25 and z₂ = 0.75 is cooled to temperature T in the two-phase region and flows into a separation chamber at a pressure of 100 kPa. If the composition of the liquid product is to be x₁= 0.175, what is the required T and what is the value of y₁. Also calculate the molar fraction of the system in the vapor phase.

Given:      lnγ₁ = 0.64 x₂²

                lnγ₂ = 0.64 x₁²

                ln(P^sat) = A - B/C + T(^oc)

where, for Acetone: A = 14.3916  ;  B = 2795.82  ;C = 230.00

  for Methanol: A = 16.5938 ;  B = 3644.30  ;  C = 239.76