1. 1. A 10 m3 tank contains steam at 275°C and 15.0 bar. The tank and its contents are cooled until the pressure drops to 1.8 bar. Some of the steam condenses in the process.

   a. How much heat was transferred from the tank?
   b. What is the final temperature of the tank contents?

2. c. How much steam condensed (kg)?

3. 2. Methane gas is burned completely with 20% excess air in a furnace operating in one atmosphere. Both the methane and air enter the furnace at 30oC saturated with water vapor. The flue gas (furnace exhaust) leaves the furnace at 1,300oC.

   a. Draw and label the process flow diagram of the process.

4. b. Show that the degree of freedom is zero.
   c. Calculate the heat lost from the furnace.

5. 3.Air at 38°C and 97% relative humidity is to be cooled to 14°C and fed into a plant area at a rate of 510 m3/min.

   a. Draw and label the process flow diagram of the process.
   b. Calculate the rate (kg/min) at which water condenses.
   c. Calculate the cooling requirement in tons (1 ton of cooling = 12;000 Btu/h),

   4. assuming that the enthalpy of water vapor is that of saturated steam at the same temperature and the enthalpy of dry air is given by the expression

6. A fuel gas containing 95 mole% methane and the balance ethane is burned completely with 25% excess air. The stack gas leaves the furnace at 900°C and is cooled to 450°C in a waste-heat boiler, a heat exchanger in which heat lost by cooling gases is used to produce steam from liquid water for heating, power generation, or process applications.

   a. Calculate the amount of heat (kJ) that must be transferred from the gas in the waste heat boiler to accomplish the indicated cooling.

   2. b. How much saturated steam at 50 bar can be produced from boiler feedwater at 40°C for the same basis of calculation? (Assume all the heat transferred from the gas goes into the steam production).

   3. c. At what rate (kmol/s) must fuel gas be burned to produce 1280 kg steam per hour (an amount required elsewhere in the plant) in the waste heat boiler?

   4. d. Calculate the volumetric flow rate (m3/s) of the gas leaving the boiler.

5. 5. An adiabatic membrane separation unit is used to dry (remove water vapor from) a gas mixture containing 10.0 mole% H2O (v), 10.0 mole% CO, and the balance CO2. The gas enters the unit at 30°C and flows past a semipermeable membrane. Water vapor permeates through the membrane into an air stream. The dried gas leaves the separator at 30°C containing 2.0 mole% H2O(v) and the balance CO and CO2. Air enters the separator at 50°C with an absolute humidity of 0.002 kg H2O/kg dry air and leaves at 48°C. Negligible quantities of CO, CO2, O2, and N2 permeate through the membrane. All gas streams are at approximately 1 atm.

   1. a. Draw and label a process diagram and carry out a degree-of-freedom analysis of the process.

   2. b. Calculate the ratio of entering air to entering gas (kg humid air/mol gas) and the relative humidity of the exiting air.

   3. c. List several desirable properties of the membrane. (Think about more than just what it allows and does not allow to permeate.)

6. 6. A mixture of n-hexane vapor and air leaves a solvent recovery unit and flows through a 70-cm diameter duct at a velocity of 3.00 m/s. At a sampling point in the duct, the temperature is 40°C, the pressure is 850mm Hg, and the dew point of the sampled gas is 25°C. The gas is fed to a condenser in which it is cooled at constant pressure, condensing 70% of the hexane in the feed.

   a. Perform a degree-of-freedom analysis of the system.
   b. Calculate the required condenser outlet temperature (°C) and cooling rate (kW).
   c. Determine the average gas velocity (volumetric flow rate divided by cross-sectional area) if the feed duct diameter were 35 cm for the same molar flow rate of the feed gas.