Question

In: Physics

(1) The HotBeverages Company has a cup that reduces the temperature of a liquid from 200...

(1) The HotBeverages Company has a cup that reduces the temperature of a liquid from 200 F to 100 F in 30 minutes by maintaining a constant temperature of 70 F.

(2) The BestSupplies Company has a cup that reduces the temperature of a liquid from 200 F to 110 F in 25 minutes by maintaining a constant temperature of 60 F.

(3) The MountainGrown Company has a cup that reduces the temperature of a liquid from 200 F to 120 F in 20 minutes by maintaining a constant temperature of 65 F.

You need to recommend which cup the restaurant should purchase. Use the questions below to make a presentation of your recommendation with a documented explanation of the recommendation to the restaurant.

(a)Use Newton’s Law of Cooling to find a function relating to the temperature of the liquid over time for each cup. ?(?) = ? ∙ ? ?? + ?? where ?(?) is the temperature of the object after a given time ? is a constant found from the initial temperature of the object ? is a constant for the continuous rate of cooling of the object

(b)Graph the three functions on a single set of axis using Excel.

(c)How long does it take each cup to lower the coffee temperature from 200 F to 130 F?

(d)How long will the coffee temperature remain between 110 F and 130 F for each cup?

(e)Eliminate one of the cups from your decision. Why did you eliminate this cup?

(f) Complete the market analysis worksheet below for the remaining two cups. What is your final probability vector? How long will it take to get to your final probability vector? What does this mean?

(g)Which company would you recommend to the restaurant? Explain your reasoning.

(h)How might the cost of the container affect your decision?

Solutions

Expert Solution


Related Solutions

200. g of liquid phase octane (C8H18) are burned in air at a temperature of 100....
200. g of liquid phase octane (C8H18) are burned in air at a temperature of 100. degrees Celsius and a pressure of 1.00 atm, forming vapor phase water and carbon dioxide. a) Write the balanced chemical reaction equation for this process. b) What is the magnitude of the difference between ΔE and ΔH for one mole of octane going through this process? (Hint: use the value of R that makes life easiest.) c) The reaction is in contact with a...
A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature...
A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 74°C, it is cooling at a rate of 1°C per minute. When does this occur? (Round your answer to two decimal places.)  min A population of protozoa develops with a constant relative growth rate of 0.9425 per member per day. On day zero the population consists of two members. Find the population size after five days. (Round your answer to the nearest whole number.) P(5) =  members
Liquid nitrogen was boiled in a styrofoam cup. Why was it critical the top of the...
Liquid nitrogen was boiled in a styrofoam cup. Why was it critical the top of the cup not be covered? What happens as the liquid nitrogen boils away? What about the temperature gradient between the top of the liquid and the top of the cup versus the temperature gradient between the liquid and the wall of the cup? What effect does frost buildup on the cup have on the shape of a weight versus time graph?
what will be the final temperature of the liquid water resulting from the mixing of 10grams...
what will be the final temperature of the liquid water resulting from the mixing of 10grams of steam at 130celcius with 40grams of ice at -10celcius? (Sp.Heat H20(s) 2.09 j/gC)(sp.heat of H20 (l) 4.18 j/gC) (sp.Heat of H20(g) 2.03 j/gC)(heat of fusion(s) 333 j/g) (heatvap H20(l) 2260 J/g)
Assume that liquid water has a temperature-independent capacity of 75 J mol-1K-1, and that for the...
Assume that liquid water has a temperature-independent capacity of 75 J mol-1K-1, and that for the transition below no heat is lost to the surroundings and the processes are reversible. a. Calculate the chnge in entropy when 1 mol of liquid water is cooled from 100C to 50 C. b. Calculate the change in entropy of the system when 1 mol of liquid water at 100C is brought into contact with 1 mol of liquid water at 0C.
A cup of hot coffee has a temperature of 201˚F when freshly poured, and is left...
A cup of hot coffee has a temperature of 201˚F when freshly poured, and is left in a room at 72˚F. One minute later the coffee has cooled to 191˚F. a. Assume that Newton's Law of cooling applies. Write down an initial value problem that models the temperature of the coffee. u'= -k(_____) u(o)= _____ b. Determine when the coffee reaches a temperature of 183˚F. Give answer in minutes, and round the answer to two decimal places.
1. How is the temperature dependence of the solubility of a solid in a liquid exploited...
1. How is the temperature dependence of the solubility of a solid in a liquid exploited to purify solids thorugh recrystalization? 2. How does temperature dependence of the solubility of a gas in a liquid affect the amount of oxygen available for fish and other aquatic animals? 3. How does the pressure dependence of the solubility of a gas in a liquid account for the bubbling that occours upon opening a can of soda?
A cup of boiling water is placed outside at 1:00pm. One minute later the temperature of...
A cup of boiling water is placed outside at 1:00pm. One minute later the temperature of the water is 152 F. After another minute its temperature is 112 F. What is the outside temperature Differential Equations(Cooling & Mixing)
A phase transition from solid to liquid takes place at constant pressure and temperature. This is...
A phase transition from solid to liquid takes place at constant pressure and temperature. This is a closed PVT system. (a) Show that the Gibbs free energy G = U - TS + PV is a constant. (b) The solid and liquid phases are in equilibrium at a temperature T and pressure P, where G(solid) = G(solid)(T,P) and G(liquid) = G(liquid)(T,P). The phases are also in equilibrium at the neighboring temperature T +dT and pressure P + dP, where G(solid)...
Someone enjoys their coffee at a temperature of 70.0C. The liquid coffe has a mass 470g...
Someone enjoys their coffee at a temperature of 70.0C. The liquid coffe has a mass 470g and must be raised in temperature by 50.0C immediately prior to enjoyment. The specific heat of water is 4.18 joules/(g * C). A standard microwave oven is used to facilitate the transfer of morning energy into the moring coffee. A) if the microwave operates at 80.0% efficiency, how much power output is actually required to perform this task in 120 seconds (answer in kW)....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT