Some equations of state can be used to predict the volume of both gases and saturated liquids. The Redlich-Kwong equation is such an equation. It can be written in polynomial form as: 𝑉𝑉3− 2−2+12 12=0
𝑉𝑉 ( ) 𝑎𝑎=0.42748𝑅𝑅2𝑇𝑇𝑐𝑐5/2𝑃𝑃𝑐𝑐 𝑏𝑏=0.08664
The equation has three roots; there can be one real root and two complex conjugate roots or three real roots. If there are three positive, real roots, the largest represents the vapor volume and the smallest represents the liquid volume. The middle one has no significance.
Use the Redlich-Kwong equation to determine the T-V diagram for n-butane from 100 K to 425K. Use 5 K temperature increments. The saturation pressure for many materials is adequately represented by the Wagner equation: 𝑙 𝑙𝑙𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑃𝑃𝑐𝑐=(1−𝑥𝑥)−1[𝐴𝐴𝐴 +𝐵𝐵𝑥𝑥1.5+𝐶𝐶𝑥𝑥3+𝐷𝐷𝑥𝑥6]
Where Psat is the saturation pressure and 𝑥𝑥=1−𝑇 𝑇 𝑐𝑐
A = -6.88709 B = 1.15157 C = -1.99873 D = -3.13003
1.A kitchen contains a standard refrigerator and a window air conditioner. The refrigerator operates at steady state using 200 W of electric power and a COP of 3. If the kitchen is well insulated:a.Will the refrigerator keep the kitchen cool without the aid of the air conditioner? Support your answer.b.If your answer in part a) is NO, then calculate the rate at which the air conditioner must remove energy from the kitchen to maintain a cool, constant temperature.2.A Carnot heat engine operates between 1000˚F and 50˚F, producing 120 BTU of work. What is the heat input to the engine?3.The heat pump for my house has a 4 kW compressor motor. I wish to keep my house at 25ºC. My house loses energy to the cold winter night at 20 kW. What is the minimum COP acceptable for my heat pump?4.The temperature inside a Carnot refrigerator is maintained at 5ºC by rejecting heat to the surroundings at an ambient temperature of 27ºC. The inside temperature now decreases to -13ºC with the ambient temperature remaining constant at 27ºC. Determine the percent increase in work input for the same quantity of heat, QL, removed.5.A thermoelectric device cools a small refrigerator and discards heat to the surroundings at 25ºC. The maximum power the device can draw is 100 W. The heat leaking through the refrigerator walls in J/sec is 30*(25 ºC - T) where T is the inside temperature of the refrigerator in ºC. Find the minimum possible value of T (in ºC) if the thermoelectric device operates with a COP = 0.6 βCARNOT.6.A multiple fuel capable heat engine operating with a low temperature of 350 K can burn Fuel “RED” or Fuel “BLUE.” Given the following information, which fuel should you use and why?
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