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 is 82 ° C. Explain and graph Ta Establish and solve an Initial Value Problem to express the water temperature as a function of time, graph this function.

Solutions

Expert Solution

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

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...

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...

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...

If we want to only use frozen water (ice) and room temperature water (room temperature water...

If we want to only use frozen water (ice) and room temperature water (room temperature water of four times the mass of the ice), write out the various forms of heat transfer that will occur between frozen water and room temperature water, when the come into contact. Hint: There will be one term of heat transfer from the room temperature water, and three terms of heat transfer in the ice/cold water.

Peas Rate of respiration Germinating, room temperature 296.1 Non-germinating, room temperature 2.122 Germinating, cool temperature 252.8...

Peas Rate of respiration Germinating, room temperature 296.1 Non-germinating, room temperature 2.122 Germinating, cool temperature 252.8 1. Compare the respiration rate among various types of seeds. 2. Compare the respiration rate among seeds that have germinated for different time periods, such as 1, 3 and 5 days

A partially filled (plastic) kettle is used to boil water. The kettle contains tap (temperature) water...

A partially filled (plastic) kettle is used to boil water. The kettle contains tap (temperature) water before it is switched on. If the thermostat to switch off the kettle when it boils is faulty: Q2d: Explain the solution strategy which would allow you to calculate the time needed to bring water to the boil. Q2a: Detail all the assumptions needed to arrive at the solution, whether they relate to equations used (i.e., the theoretical basis) or any values which must...

1. A hot solution of a particular compound was allowed to cool to room temperature. After...

1. A hot solution of a particular compound was allowed to cool to room temperature. After waiting a few minutes, it was noticed that the crystallization had not taken place. Discuss two ways to induce crystallization. 2. What properties are necessary and desirable for a solvent in order that it is well suited for recrystallizing a particular organic compound? 3. Assume that 3.0 g of aniline and 4.5 ml of acetic anhydride are used in the preparation of acetanilide. What...

An air conditioning company servicing a certain machine room guarantees that the temperature in the room...

An air conditioning company servicing a certain machine room guarantees that the temperature in the room stays below 20o C. Due to malfunctioning of the equipment operating in the machine room, it is suspected that the average temperature actually exceeds 20o for more or less extended periods of time. Seven temperature measurements are collected throughout the day and the following temperatures are observed, 20.8, 20.2, 20.9, 21.5, 22.2, 21.2, 19.8. Assuming that the temperature is at least approximately normally distributed,...

At what temperature will water boil at Lake Tahoe? Lake Tahoe is approximately 1900 m above...

At what temperature will water boil at Lake Tahoe? Lake Tahoe is approximately 1900 m above the sea level. The molar mass of air is 29.0 g/mol. Assume that air pressure at sea level is 1.00 atm and the air temperature is constant with elevation at 20 degrees Celsius. The molar heat of vaporization of water is 41.0 kJ/mol.

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 = ?

Subjects