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Solved Problems in Thermodynamic Property Relations
1.) Verify the validity of the Maxwell relation IV (Eq. 3.20)
for steam at 250C and 300 kPa.
Solution:
[ ] [ ] from steam tables:
2.) Using the Clausius-Clapeyron equation, estimate the value of
the enthalpy of vaporization of
refrigerant-134a at 20C.
Solution:
from refrigerant tables:
( )
substituting these values to the equation for h fg :
The actual value of h fg is 181.09 kJ/kg.
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3.) Estimate the saturation pressure of refrigerant-134a at-50F,
using the data available in therefrigerant tables.
Solution:Using the Clausius-Clapeyron equation the saturation
pressure can be extrapolated in the
absence of a compete table.
integrating the Clausius-Clapeyron equation:
let T 1 = -40F and T 2 = -50F
The actual value of the saturation pressure p2 at -50F is 5.505
psia.
4.) Show that for an ideal gas.
Solution:
This relation is proved by showing that the right-hand side of
(5.31) is equivalent to thegas constant R of the ideal gas:
subtituting:
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5.) Show that the Joule-Thompson coefficient of an ideal gas is
zero.
Solution:
* +
For an ideal gas , and thus substituting:
* + [ ] 6.) Determine the enthalpy change and entropy change of
oxygen per unit mole as it undergoes a
change of state from 220K and 5 MPa to 300K and 10 MPa (a) by
assuming ideal-gas behavior and (b) by accounting for the deviation
from ideal-gas behavior.
Solution:(a) The enthalpy values at the initial and the final
temperatures can be determined from
the ideal-gas table at the specified temperatures:( ) ( ) The
entropy depends on both temperature and pressure even for ideal
gases. Under theideal-gas assumption, the entropy change of oxygen
is determined from
where:
(b) The deviation from the ideal-gas behavior can be accounted
for by determining theenthalpy and entropy from the generalized
charts at each state:
}
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and
} Then, ( ) and
7.) Using p-v-T data for saturated water, calculate the (a)
latent heat of vaporization at 100Cand (b) s g s f .
Solution:(a)
from steam tables:
* + This agrees very closely with the value read from the steam
tables, h fg = 2257 kJ/kg.
(b)
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8.) Determine the u g u f of water at 100C.
Solution:
since vaporization occurs at constant pressure:
( ) from steam tables:
9.) For liquid water at 1 atm and 20C, estimate the percent
error in cv that would result if it
were assumed that c p = cv.
Solution:
10.) Using h fg , v fg and p sat at 10F from the
refrigerant-134a tables, estimate the saturation
pressure at 20F.
Solution:
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integrating the above equation yields:
:Reference:
Y. A. Yunus and M. A. Boles. Thermodynamics: An Engineering
Approach, 4 th Ed. NewYork: McGraw-Hill, 2002.
M. J. Moran and H. N. Shapiro. Fundamentals of Engineering
Thermodynamics, 5 th Ed.John Wiley & Sons, Inc., 2004.
