1. An employee at General Electric must order bottles of compressed methane to run her gas oven test facility. The bottles have an internal volume of 200 liters and come at gage pressures of 17 MPa. The oven test facility requires 2 g/s of methane. Assume the temperature is constant at 300 K.
a) If the engineer uses the ideal gas law to calculate the mass in the bottle, how many minutes and seconds does she calculate that she can run her oven test facility on one bottle?
b) If she instead uses the general compressibility chart, how long does she think she can run? Based on this number how accurate is the ideal gas law.
2. A bottle with 200 liters of CO2 is initially at 3000 kPa and 300 K. Inside the bottle, an electric heater made of Nichrome wire (mwire = 0.2 kg) is supplied with an electrical current of 10 Amps at a voltage difference of 42 V. The Nichrome wire loses heat to the surrounding CO2 gas. For this problem, assume that the Nichrome wire has a constant CV,wire = 480 J/kg·K. For the CO2, assume that the gas has a common uniform temperature T CO2 and further a constant CV,CO2 = 745 J/kg*K that is independent of T. The ambient temperature outside the bottle Tamb = 300 K.
a) Initially everything is at 300 K before the current flows through the wire. What is the initial rate of temperature rise of the Nichrome wire when the current begins to flow?
b) How accurate is the ideal gas model for predicting the mass of CO2 and what is the mass of CO2 inside the container using generalized compressibility chart?
c) If the current is supplied continuously, the CO2 temperature will reach a steady state when dTCO2/dt = 0. What is Twire, TCO2 and pCO2 in the container at the steady state condition?
Note that to find pCO2, you should use the generalized compressibility chart.
3. High pressure steam at 1.2 MPa and 400ºC is inside a closed stainless steel vessel with an internal volume of 200 liters. The stainless steel vessel has a mass of 20 kg and is in equilibrium with the H2O.
The H2O and stainless steel cool to 50ºC. The stainless steel has a constant Cp of 0.48 kJ/kg*K.
a) What is the final quality of the H2O inside the vessel?
b) How much heat is transferred to the surroundings by the cooling of the reactor and the H2O together?