## Problems

2.1 One kilogram of steam, initially at 200°C and 1 atm (state 1), is cycled through the following processes:

2—»3. Cool to 400°C with simultaneous pressure increase to 5 atm along a straight-line path in p-v coordinates.

3—»4. Return to 200°C at 2 atm via two subprocesses: decrease pressure at constant temperature, then decrease temperature at constant pressure. (Hint: you will need to perform a numerical integration for the first subprocess of step 3—>4.)

\Vhat are the volume changes and heat requirements for each process?

2.2 The specific volume of a three-phase mixture of ice, liquid water, and water vapor at the triple point is v m3/kg and the specific internal energy is u kJ/kg.

(a) Using Tables A.l and A.5, prepare a table giving v and u for the three phases.

(b)For given u and v what are the equations that determine the mass fractions of water in the three phases y, 2 for vapor, liquid and solid, respectively). Assume that the specific volumes of the condensed phases are negligible compared to that of the vapor.

(c) Plot an existence diagram that shows the region of permissible values of u and v.

2.3 A 10-kg specimen of copper is quenched ai constant pressure from 700°C in a 100-liter, adiabatic water bath initially at 20°C. Neglecting the heat capacity of the container and vaporization of water, what is the final temperature of the system?

2.4 The isotherm passing through the critical point in the p-v diagram of Figure 2.9 has the following mathematical properties:

(a) Use the values of the Van der Waals constants a and b given in the text to determine the critical pressure and temperature of N2. (Hint: to solve the equations, use the dimensionless critical volume X ~ VJb and dimensionless critical temperature Y = TJ(a/Rb).)

(b) Compare the values of pc and Tc so calculated with the values reported in the Handbook of Physics and Chemistry (CRC Press, 2006) of pc = 3.35 MPa, Tc = 126 K.

2.5 An initially deflated balloon is connected by a valve to a tank containing helium at 1 MPa and 20°C. When the valve is opened and the gas equilibrates between the tank and the balloon, the diameter of the balloon is 4 m, the pressure is 4 kPa and the temperature is unchanged. What is the volume of the tank?

2.6 Nitrogen behaves as a Van der Waals nonideal gas. The experimentally-determined compressibility of N2 is shown in Figure 2.3.

(a) Using Equation (2.4), determine the coefficients a and b from points A and B in Figure 2.3.

(b) Using the parameters determined in part (a), compare the accuracy of the approximate form, Equation (2.5a), with the full form, Equation (2.3), at 150 K and 1 MPa.

2.7 A pump delivers 50 kg/s of water at 300°C and 20 MPa.

(a) What is the volume flow rate in m3/s?

(b) If the properties of saturated liquid water at 300°C were used in the calculation, what is the error in the calculation of (a)?

(c) If the properties of saturated liquid water at 20 MPa were used, what would the error be?

2.8 Determine whether water in the following states is a compressed liquid, a superheated vapor, or a two-phase mixture of liquid and vapor:

Temp . °C Pressure, kPa Specific vol., mVkg