Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation dT = k(T – A), where T is the temperature of the object after t units of time have passed, A is the ambient dt temperature of the object's surroundings, and k is a constant of proportionality. Suppose that a cup of coffee begins at 179 degrees and, after sitting in room temperature of 66 degrees for 15 minutes, the coffee reaches 169 degrees. How long will it take before the coffee reaches 156 degrees? Include at least 2 decimal places in your answer.

Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation dT = k(T – A), where T is the temperature of the object after t units of time have passed, A is the ambient dt temperature of the object's surroundings, and k is a constant of proportionality. Suppose that a cup of coffee begins at 179 degrees and, after sitting in room temperature of 66 degrees for 15 minutes, the coffee reaches 169 degrees. How long will it take before the coffee reaches 156 degrees? Include at least 2 decimal places in your answer.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter1: Units And Measurement

Section: Chapter Questions

Problem 10CQ: For each of the following scenarios, refer to Figure 1.4 and Table 1.2 to determine which metric...

See similar textbooks

Similar questions

The average life expectancy in Japan is 81 years. What is this time in SI units?
For each of the following scenarios, refer to Figure 1.4 and Table 1.2 to determine which metric prefix on the meter is most appropriate for each of the following scenarios. (a) You want to tabulate the mean distance from the Sun for each planet in the solar system. (b) You want to compare the sizes of some common viruses to design a mechanical filter capable of blocking the pathogenic ones. (c) You want to list the diameters of all the elements on the periodic table. (d) You want to list the distances to all the stars that have now received any radio broadcasts sent from Earth 10 years ago. 1.2 Units and Standards
The quantity of energy Q transferred by heat conduction through an insulating pad in time interval Δt is described by Q/Δt = κAΔT/d, where κ is the thermal conductivity of the material, A is the face area of the pad (perpendicular to the direction of heat flow), ΔT is the difference in temperature across the pad, and d is the thickness of the pad. In one trial to test material as lining for sleeping bags, 86.0 J of heat is transferred through a 3.40-cm-thick pad when the temperature on one side is 37.0°C and on the other side is 2.00°C. In a trial of the same duration with the same temperatures, how much heat will be transferred when more of the material is added to form a pad with the same face area and total thickness 8.41 cm?
Scientists are studying the temperature on a distant planet. They find that the surface temperature at one location is 25° Celsius. They also find that the temperature decreases by 3° Celsius for each kilometer you go up from the surface. Let T represent the temperature (in Celsius), and let H be the height above the surface (in kilometers). Write an equation relating T to H, and then graph your equation using the axes below. * T axis (y) goes up to 30 (counting by 5's) * H axis(x) goes up to 8 (counting by 1's) **Be sure to write out the points too
The equation for the ideal gas is (P – a/V2) (V-b) = K. Here P is the pressure, V is the volume of the gas. If a and b are constants, what is the the units of a/b.
A picture window has dimensions of 1.25 m by 2.6 m and is made of glass 7.5 mm thick. On a winter day, the outside temperature is 22° C while the inside temperature is a comfortable at 19° C. (k of glass =0.075W/m.K) Calculate the following:a) the area of the window in square metres
Heat Q, which has the SI unit of joule (J), is the quantity in mechanical engineering that describes the transit of energy from one location to another. The equation for the flow of heat during the time interval At through an insulated wall is KAAT Q = (Тh — T) where k is the thermal conductivity of the material from which the wall is made, A and L are the wall's area and thickness, and Th – T; is the difference (in degrees Celsius) between the high- and low-temperature sides of the wall. By using the principle of dimensional consistency, what is the correct dimension for thermal conductivity in the SI? The lowercase Greek character kappa (K) is a conventional mathematical symbol used for thermal conductivity. Appendix A summarizes the names and symbols of Greek letters. О a. (W-m)/°C O b. °C/(W. m) O c. (m . °C)/W O d. W/(m . °C)
One mole of Gold (Au) atom has a mass of 197 g. We know that the density of gold is 19.30 g/cm3 in room temperature. Using those numbers, answer the following questions: a) What is the mass of a single gold atom in kg? b) Assume that gold atoms sit in a perfect cubic crystal structure. Estimate the distance between two gold atoms in meters. c) If we have a gold cube of 6 cm on each side, how many atoms can we fit along the edge of each side of the cube? d) What would be the mass, in kilograms, of the gold cube we discussed in part (c) (measuring 6 cm on each side)?
According to the Ideal Gas Law, PV = KT, where P is pressure, V is volume, T is temperature (in kelvins), and k is a constant of proportionality. A tank contains 1300 cubic inches of nitrogen at a pressure of 40 pounds per square inch and a temperature of 300 K. (a) Determine k. k = (b) Write P as a function of V and T and describe the level curves. P = Setting P = c, the level curves are of the form V =
Estimate how many molecules of air are in each 2.5-L breath you inhale that were also in the last breath Galileo took. [Hint: Assume the atmosphere is about 10 km high and of constant density.] Express your answer using two significant figures. N=?? (I got 27, but I was also wrong).
The volume of an automobile tire is 2.5x10^-2m^3. The pressure of the air in the tire is 3.3 atm and the temperature is 25C°. What is the mass of air in grams? The mean molecular mass of air is 29g. Calculate to 2 decimals.
You are looking at a thermometer that has a mark for each degree. You are going to write down a number corresponding to the temperature. How will you decide how many significant figures to use in the number? (i.e. Will you report the temperature to the ones place, tenths, hundredths, other?)