Chapter 6, Problem 6.3P

(5) Consider a gas that follows the equation of state NRT aN? p = V – bN V2 | 8a This is called van der Waals gas (a,b > 0). For temperatures T > Tc = p(V) is a 27RB monotonic decreasing function. Assume T > Tc and Cy = 3NR/2. Consider an insulated box with volume V, . The box was divided by a wall. One of the compartments had volume Vo at temperature To, filled with van der Waals gas of amount N, and the other was vacuum. The system was in equilibrium. (a) The wall was removed abruptly. The gas expanded and occupied the entire box. This process is called adiabatic free expansion. The temperature in the box is now T, in equilibrium. What is T, – T,? (b) The internal energy of the gas does not change by adiabatic free expansion. Why? (c) Instead of the abrupt removal, the wall was moved through adiabatic and quasi-static process, and the gas expanded to the entire volume of the box. The temperature in the box is now T, in equilibrium. What is T2? (d) Show T, > T2, using the arguments of…

2. Given a closed container of volume 1 L containing 50 g of helium gas, calculate the following: a. The pressure at T = 6 K, assuming that the gas is an ideal gas. b. The pressure at T of state. = 6 K, assuming that the gas obeys van der Waal's equation c. The pressure at T 6 K, assuming that the gas obeys the virial equation of state truncated after the second term. = d. The state of the fluid at T = 4.2 K. (Hint: 4.2 K is below T. and 50 kg/m³ is greater than p, @ 4.2 K.)

2) Using the tables for water, determine the specified property data at the indicated states. In each case, locate the state on a sketch of the p–v diagram. a)At p = 3 bar, v= 0.5 m3/kg, find T in °C and u in kJ/kg. b)At T = 320°C, v= 0.03 m3/kg, find p in MPa and u in kJ/kg. c)At p = 28 MPa, T = 520°C, find in m3/kg and h in kJ/kg.

● Determine the missing properties and the phase descriptions in the following table for water: T, °C 125 75 P, KPa 200 1000 500 800 u, kJ/kg 1600 2950 X 0.6 0.0 Phase Description

TOPIC: PRIOPERTIES OF SUBSTANCES:Note: The pressure values are absolute values unless specified.Determine the properties of H2O with units according to the following Table: Provide the complete solution

4. A vessel with 8.0 g of helium gas follows the two-step process, 123, shown in the figure to the right. a) Qualitatively describe what is being done to the gas vessel in the two processes. b) Find the values of V₁, V3, P2, and T3. P2 2 atm 0 P 657°C 2 37°C- 1 V₁ Isothermal 3 V3 V

HW1- Complete the following table for H₂O. Write the details of the solution and show each state on a Tv diagram State T, °C 2 3 5 140 125 500 P, kPa 550 750 500 v, m³/kg 0.05 0.140 h, kJ/kg phase description 2890 Saturated liquid

3. Find the internal energy of water at the given states for 6 MPa and determine: T,°C U, KJ/Kg Phase Description saturated vapor State 1 State 2 saturated liquid saturated liquid saturated vapor state 3 + 0.95 state 4 500°C state 5 100°C state 6 T= 460°C a- The internal energy b-and the phase descriptions in the following table for water.

1)Using the tables for water, determine the specified property data at the indicated states. In each case, locate the state on a sketch of the T–v diagram. a)At p = 2 MPa, T = 300 °C. Find u, in kJ/kg. b)At p = 2.5 MPa, T = 200 °C. Find u, in kJ/kg. c)At T = 170°F, x = 50%. Find u, in Btu/lb.