A 63 g bullet is fired from a height of 350 m. The initial speed of the bullet is 185 m/s. The bullet eventually comes to rest in a bucket containing 1.7 kg of mercury that is at ground level. As a result of bringing the bullet to a stop (any change in PE while in the mercury is negligible), how much does the temperature of the mercury increase (express the answer in K)? Also determine how fast the bullet is going at impact. Ignore air drag and assume that all of the thermal energy generated goes into heating the mercury. (note thhe specific heat of mercury is 140 (J/kg·K). Impact speed = ΔT =

You drop an ice cube into an insulated flask full of water and wait for the ice cube to completely melt. The ice cube initially has a mass of 90.0 g and a temperature of 0°C. The water (before the ice cube is added) has a mass of 850 g and an initial temperature of 22.0°C. What is the final temperature (in °C) of the mixture? (Assume no energy is lost to the walls of the flask, or to the environment.)  °C

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.

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?