Water is boiled in a cup and its placed in a room that is 25 degrees...

Water is boiled in a cup and its placed in a room that is 25 degrees Celsius. Assume that Newton's Law of Cooling is satisfied: the rate of change in water temperature is proportional to the difference between the temperature of the water and the temperature of the environment. We take the water temperature after 7 minutes and find it to be 77 degrees Celsius. Establish and solve an initial value problem to express the temperature of the water as a function of time, graph this function and calculate when the water temperature reaches 26 degrees Celsius.

Expert Solution

Colby Messinger answered 1 year ago

Water is boiled in a cup and put to cool down inside a room. The air...

Water is boiled in a cup and put to cool down inside a room. The air temperature in the room is increasing linearly according to the function Ta(t) = 22 + 0.015t (t in minutes, T in Celsius). Assume Newton’s Law of Cooling is satisfied: the rate of change of water temperature is proportional to the difference between the temperature of the water and the temperature of the environment. The temperature of the water was checked after 8 minutes and...

250 gallons of water (at 25 degrees Celsius and 1 atmospheric pressure) are boiled to power...

250 gallons of water (at 25 degrees Celsius and 1 atmospheric pressure) are boiled to power a steam engine. The heat source to boil the water is the combustion of methanol according the the reaction below. 2 CH3OH (liters) + 3 O2 (grams) −→ 2 CO2 (grams) + 4 H2O (liters) Using the enthalpy of the combustion of methanol (at 25 degrees Celsius and 1 atmospheric pressure), how many liters of methanol are required to boil the 250 gallons of...

Water is boiled in a bowl and cooled in a room. The air temperature in the...

Water is boiled in a bowl and cooled in a room. The air temperature in the room is increasing linearly according to the function Ta(t) = 30 + 0.01t (t in minutes, T in ∘C. Assume that Newton's Law of Cooling is satisfied: the rate of change of the temperature of the water is proportional to the difference between the temperature of the water and the temperature of the environment. We take the temperature of the water after 10 minutes...

A cup of coffee is made with boiling water at 100 and stands in a room...

A cup of coffee is made with boiling water at 100 and stands in a room where the temperature is 25. The change in temperature, H in degrees , with respect to time t, in minutes, is given by the following differential equation. (dH)/(dt)=-k(H-25) Solve this differential equation. If the coffee cools to 90 in 3 minutes, how long will it take to cool to 60 degrees? Round your answer to the nearest integer.

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?

Newton's Law of Cooling: Boil water in a cup and cool in a room at 32∘C....

Newton's Law of Cooling: Boil water in a cup and cool in a room at 32∘C. Assume that Newton's Law of Cooling is satisfied: the rate of change of water temperature is proportional to the difference between the temperature of the water and the temperature of the environment. We take the water temperature after 5 minutes and find it to be 83∘C. Establish and solve an Initial Value Problem to express the water temperature as a function of time, graph...

A beaker of water at 80 degrees celsius is placed in the center of a well-insulated...

A beaker of water at 80 degrees celsius is placed in the center of a well-insulated room whose air temperature is 20 degrees celsius. Is the final temperature of the water: A) 20 degrees celsius B) Slightly above 20 degrees celsius C) 50 degrees celsius D) Slightly below 80 degrees celsius E) 80 degrees celsius

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 metal bar, initially at 2000K, is placed in a large tank of water at room...

A metal bar, initially at 2000K, is placed in a large tank of water at room temperature. Tank is well isolated from the environment. Between the moment bar was placed in the water and the moment when bar and water reached equilibrium, did the entropy of the metal bar increased, decreased, or remained the same? Explain.

Assume a cup contains about 12 oz or 340 g of water at room temperature, about...

Assume a cup contains about 12 oz or 340 g of water at room temperature, about 20 degree C. The electric kettle draws energy from the wall outlet at a rate (Power) of 990W. Draw a single Energy-Interaction Diagram for the process of bringing the water to a rolling boil. Choose an appropriate physical system, as well as an initial and a final point in time and indicate all initial and final conditions on your timeline. Explicitly state any other...

Question