Thermodynamic Properties of Fluids

ECHE 311/SPRING 2015 Problem Set # 4 Thermodynamic Properties of Fluids

1. Estimate the change in enthalpy and entropy when liquid ammonia at 270oK is compressed from its saturation pressure of 328 kPa to1,200 kPa. For saturated liquid ammonia at 270oK, Vl=1.551x10-3 m3kg-1, and  =2.095x10-3K-1.

Hint: At constant temperature the Eqs. in your textbook are written as:

dS  VdP and dH  (1 T )VdP

2. Liquid water at 25oC and 1 bar fills a rigid vessel. If heat is added to the water until its temperature reaches 50oC, what pressure is developed? The average value of  between 25 and 50oC is 36.2x10-5 K-1. The value of  at 1 bar and 50oC is 4.42x10-5 bar-1, and may be assumed independent of P. The specific volume of liquid water at 25oC is 1.0030 cm3g-1.

Hint/Suggestion. Use constant volume change equation from your textbook:

 (T2  T1)   (P2  P1)  0

3. Estimate the entropy change of vaporization of benzene at 50oC. The vapor pressure of benzene is given by the Antoine equation:

2,788.51 lnPsat / kPa  13.8858  P(50) =36.166 kPa t/o C  220.79

d P( t ) 1.375 dPdt=1.375 kPa/K dt

 Use the Clapeyron Eq. dP/dT=  Hlv/T  Vlv with an estimated value of Vlv.

dln Psat  Use the Clausius/Clapeyron Eq Hlv=- R d(1/ T )

Hint/Suggestion: (a) The entropy change of vaporization is equal to the latent heat divided by the temperature. For the Clapeyron we need the volume change of vaporization. For this we estimate the liquid volume by Racket equation and the vapor volume by the generalized virial correlation:

o P1 P Z1  Br   B r or Tr T r

RT Pr Vvap[1  ( B o  B1 ) P Tr

Solve Clapeyron for the latent heat and divide by T to get the entropy change of vaporization. RT (b) S= dPdt P

4. A two phase system of liquid and water and water and vapor in equilibrium at 8,000 kPa consists of equal volumes of liquid and vapor. If the total volume Vt=0.15 m3, what is the total enthalpy Ht and what is the total entropy St. (Data Table F.3)

Hint: Htotal = mliqHliq+ mvapHvap

5. Wet stream at 230oC has a density of 0.025 g cm-3. Determine x, H and S. (Data Table F.1 and 230oC.)

V Vliq Hint: x  Vvap Vliq

6. Steam at 2,100 kPa and 260oC expands at constant enthalpy to 125 kPa. What is the temperature of the steam in its final state and what is the entropy change? If steam were an ideal gas, what would be its final temperature and entropy change?

Hint/Suggestion: Take Data from the Steam Table at 2,100 kPa and 260oC by interpolation. Final state is at enthalpy H1 and a pressure of 125 kPa. For steam as an ideal gas, there would be no temperature change.