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 T_a(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 it was 82 Celsius. Explain and graph T_a. Establish and solve an Initial Value Problem to express the water temperature as a time function, graph this function.

Expert Solution

genius_generous answered 2 years ago

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...

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...

Boil water in a bowl and cool in a room. The air temperature in the room...

Boil water in a bowl and cool in 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 ° 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 8 minutes and find that it...

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...

Take a hard boiled egg or tippee top and put it lying down on a table...

Take a hard boiled egg or tippee top and put it lying down on a table and start to spin it, if you spin it fast enough it will start to spin in an upright position. How do the egg, and tippee top remain stable in their rotating positions? What other toys can you think of are based on interesting quirks of physics? (Try to explain the physics behind them!)

A- a small volume of cold water is used to cool off a cup of coffee...

A- a small volume of cold water is used to cool off a cup of coffee that is initially too hot to drink. How many mL of water at 4.0oC must be mixed with 485 mL of hot coffee (95.0oC) so that the resulting combination has a temperature of 70.0oC? Assume that the coffee and water have the same density and specific heat. B- A 5.00 cm3 sample of aluminum at room temperature (25.00oC) was dropped into a 1 L...

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.

In a closed room, you turn the ceiling fan on to cool yourself down as you...

In a closed room, you turn the ceiling fan on to cool yourself down as you complete an online exam. Over time, will the temperature in the room increase/decrease/stay the same? Support your answer using explanations/equations as necessary.

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?

A thermometer is taken from an inside room to the outside, where the air temperature is...

A thermometer is taken from an inside room to the outside, where the air temperature is −15° C. After 1 minute the thermometer reads 13° C, and after 5 minutes it reads −1° C. What is the initial temperature of the inside room? (Round your answer to two decimal places.) c = ?

Question