problem 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:
C_{p }= C_{v } + T(∂P/∂T)_{V} (∂V/∂T)_{P}
problem 2: Liquid isobutane is throttled through a valve from 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:
V = V_{c}Z_{c}^{(1-Tr)^0.2857}
Given: V_{c }= 262.7 cm^{3}/mol, Z_{c}= 0.282 and T_{c}= 408.1 K
Also, change in T and V is negligible during throttling process.
problem 3: A concentrated binary solution containing mostly species 2 (but x_{2} 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 x_{1} and y_{1}.
Given: H_{1} = 200 bar, P_{2}^{sat} = 0.1 bar
State and justify all assumptions.
problem 4: For the acetone(1)/methanol(2) system a vapor mixture for which z_{1} = 0.25 and z_{2} = 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 x_{1}= 0.175, what is the required T and what is the value of y_{1}. Also find out the molar fraction of the system in the vapor phase.
Given:
lnγ1 = 0.64 x_{2}^{2}
lnγ2 = 0.64 x_{1}^{2}
ln(P^{sat}) = A – B/(C + T(°C))
Where, for Acetone: A = 14.3916; B = 2795.82; C = 230.00
for Methanol: A = 16.5938; B = 3644.30; C = 239.76