Kool-Aid contains Allura Red dye. A student makes a Kool-Aid solution by diluting 61.2 mg of Kool-Aid with water to a total volume of 25.00 mL using a volumetric flask. Because this solution is too concentrated (measured absorbance > 1.0), the student then dilutes a small sample of the Kool-Aid solution by taking 0.500 mL of the solution and mixing it with 0.500 mL of water (a ½ dilution). The absorbance of the ½ diluted solution is 0.315. Using the Beer’s Law curve, determine the concentration of the dye in the original Kool-Aid.

Amass of 1.5 kg of air at 120 kpa and 24°c is contained in a gas-tight, frictionless piston-cylinder device. the air is now compressed to a final pressure of 720 kpa. during the process, heat is transferred from the air such that the temperature inside the cylinder remains constant. calculate the boundary work input during this process.

Air is compressed isentropically from an initial state of 300 k and 101 kpa to a final temperature of 1000 k. determine the final pressure using the following approaches: (a) approximate analysis (using properties at the average temperature) (b) exact analysis

Tom is having a problem with his washing machine. he notices that the machine vibrates violently at a frequency of 1500 rpm due to an unknown rotating unbalance. the machine is mounted on 4 springs each having a stiffness of 10 kn/m. tom wishes to add an undamped vibration absorber attached by a spring under the machine the machine working frequency ranges between 800 rpm to 2000 rpm and its total mass while loaded is assumed to be 80 kg a) what should be the mass of the absorber added to the machine so that the natural frequency falls outside the working range? b) after a first trial of an absorber using a mass of 35 kg, the amplitude of the oscillation was found to be 10 cm. what is the value of the rotating unbalance? c) using me-3.5 kg.m, find the optimal absorber (by minimizing its mass). what would be the amplitude of the oscillation of the absorber?