160 grams of boiling water (temperature 100° C, heat capacity 4.2 J/gram/K) are poured into an aluminum pan whose mass is 900 grams and initial temperature 21° C (the heat capacity of aluminum is 0.9 J/gram/K). (a) After a short time, what is the temperature of the water? Tfinal = (b) What simplifying assumptions did you have to make? The thermal energy of the aluminum doesn't change. The thermal energy of the water doesn't change. The heat capacities for both water and aluminum hardly change with temperature in this temperature range. Energy transfer between the system (water plus pan) and the surroundings was negligible during this time. (c) Next you place the pan on a hot electric stove. While the stove is heating the pan, you use a beater to stir the water, doing 29640 J of work, and the temperature of the water and pan increases to 84.6° C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan? Q = J

We know from Newton's Law of Cooling that the rate at which an object warms up is proportional to the difference between the ambient temperature of the room and the temperature of the object. The differential equation corresponding to this situation is given by y' = k(M – y) where k is a positive constant. The solution to this equation is given by y = M + (yo – M)e-kt , where yo is the initial temperature of the object. Suppose your Thanksgiving turkey is kept at a temperature of 40 degrees Fahrenheit until it is put into a 350 degree Fahrenheit oven. It takes 2 hours for the turkey to warm up to a safe eating temperature of 165 degrees Fahrenheit. Find the values of yo, M, and k, for this situation, rounding your answers to 3 decimal places. Yo= M = k= Regardless of your answers above, suppose the k value in this situation is k = 0.3. Find the initial rate of increase of the turkey's temperature as soon as it is placed in the oven. Round to 3 decimal places. degrees per hour.

Assume Lake Michigan contains 4.90 x 1012 m³ of water, and assume the water's density is that of water at 20°C and 1 atm. (a) How much energy (in J) is required to raise the temperature of that volume of water from 12.2°C to 24.4°C? 4.1E19 From the density of water and the volume, what is the mass of the water? What is specific heat? How is it related to the energy input, mass, and temperature change? Use it to solve for the energy. Be careful with units. J (b) How many years would it take to supply this amount of energy by using a power of 1,400 MW generated by an electric power plant? 926 How is power related to energy and time? Knowing the energy from part (a), can you find the time? Be careful with units. Make sure you convert the time in seconds to years. yr

A mass m of a metal with heat capacity CM at initial temperature T is added to the volume V of a liquid with density p and heat capacity c₁ at initial temperature T₁. What is the final temperature of the system?