The specific heat of an object can be measured by placing it in thermal contact with another object whose specific heat is known. As an example, suppose that a chunk of metal, whose mass is 0.21 kg, is immersed in boiling water (100 °C) until it reaches thermal equilibrium, at which time it has a temperature of 100 °C. The chunk of metal is then quickly transferred into a styrofoam (insulating) cup containing 0.18 kg of water at 20 °C. After a minute or so, the temperature of the contents of the cup stabilizes at 33 °C. Assume that once the metal is added to the cup the only energy transfer is between the hot metal and the colder water. In other words, there are no significant energy transfers to either the cup itself or to the surroundings. The specific heat of water in the relevant range of temperature is roughly 4.2 kJ kg 1 °c-1 Question: What is the specific heat of the metal (in units of kJ kg1 °C-1, but do not include units in your answer)? Hint: Solving this problem requires 4 steps: 1) Calculate the amount of heat gained by the water. 2) Use energy conservation to relate the heat gained by the water to the heat lost by the metal. This should determine the heat lost by the metal. 3) Use the heat lost by the metal and its temperature change to calculate the heat capacity of the metal. 4) Use the heat capacity of the metal and its mass to calculate the specific heat of the metal in SI units (kJ kg1 °C-1). Do not include units in your answer. Write your answer as a number in normal form as described in the instructions at the top of this worksheet.

A 390-g metal container, insulated on the outside, holds 170.0 g of water in thermal equilibrium at 21.0°C. A 18.0-g ice cube, at -15.0°C, is dropped into the water, and when thermal equilibrium is reached the temperature is 12.0°C. Assume there is no heat exchange with the surroundings. The specific heat capacity of water is 4190 J/kg ∙ K, the specific heat capacity of ice is 2090  J/kg ∙ K and the heat of fusion is 3.34 × 105 J/kg. What is the specific heat capacity of the metal of the container?

An insulated container is partly filled with oil. The lid of the container is removed, 0.150 kg of water heated to 84.0°C is poured in, and the lid is replaced. As the water and the oil reach equilibrium, the volume of the oil increases by 1.00x105 m³. The density of the oil is 919 kg/m³, its specific heat capacity is 1980 J/(kg-C°), and its coefficient of volume expansion is 726x10-6 (Cº)-¹. What is the temperature when the oil and the water reach equilibrium? Number Units

A 0.250-kg aluminum bowl holding 0.800 kg of soup at 26.6°C is placed in a freezer. What is the final temperature if 420 kJ of energy is transferred from the bowl and soup? Assume the soup has the same thermal properties as that of water, the specific heat of the liquid soup is 1.00 kcal/(kg · °C), frozen soup is 0.500 kcal/(kg · °C), and the latent heat of fusion is 79.8 kcal/kg. The specific heat of aluminum is 0.215 kcal/(kg · °C).

A copper block with a mass of 400 grams is cooled to 77 K by being immersed in liquid nitrogen. The block is then placed in a Styrofoam cup containing some water that is initially at +50.0°C. Assume no heat is transferred to the cup or the surroundings. The specific heat of liquid water is 4186 J/(kg °C), of solid water is 2060 J/(kg °C), and of copper is 385 J/(kg °C). The latent heat of fusion of water is 3.35 x 105 J/kg. What is the mass of water in the cup, if the final temperature is -25.0°C?

A block of metal of mass 0.200 kg is heated to 152.0°C and dropped in a copper calorimeter of mass 0.250 kg that contains 0.150 kg of water at 30°C. The calorimeter and its contents are insulated from the environment and have a final temperature of 46.0°C upon reaching thermal equilibrium. Find the specific heat of the metal. Assume the specific heat of water is 4.190 × 103 J/(kg · K) and the specific heat of copper is 386 J/(kg · K). J/(kg · K)

Ice at 0 °C is placed in a Styrofoam cup containing 0.62 kg of lemonade at 32 °C. The specific heat capacity of lemonade is virtually the same as that of water; that is, c = 4180 J/(kg C°). After the ice and lemonade reach an equilibrium temperature, some ice still remains. The latent heat of fusion for water is Lf = 3.35 x 105 J/ kg. Assume that the mass of the cup is so small that it absorbs a negligible amount of heat, and ignore any heat lost to the surroundings. Determine the mass of ice that has melted, in grams.

Water is placed into an iron container along with an ice cube. They are thermally isolated.The iron container has a mass of 790. g and is initially at 72.0 degrees Celsius. The water has a mass of 220. g and is initially at 17.0 degrees Celsius. The ice cube has a mass of 80.0 g and is initially at -15.0 degrees Celsius.What is the heat required to raise the temperature of the ice to 0 degrees Celsius?

A 0.100 kg piece of ice at initial temperature −5.00 ◦C is placed in a perfectly insulated container with 1.00 kg (1 L) of water at initial temperature 20.0 ◦C. The container absorbs or releases no heat. All of the ice melts as the system reaches an equilibrium temperature Tf .  How much heat must the ice exchange with the rest of the system to raise its temperature to the melting point, 0.00 ◦C? Would this heat exchanged be positive, zero, or negative? Once the ice reaches its melting point, how much heat must the ice exchange with the rest of the system to melt? Would this heat exchanged be positive, zero, or negative? Once the ice melts, it is liquid water at 0.00 ◦C. Write an expression for the heat exchanged by the newly-melted ice QI to reach the equilibrium temperature Tf . Would you expect QI to be positive, zero, or negative? Write an expression for the heat exchanged by the original water QW to reach the equilibrium temperature Tf from its initial temperature. Assuming no…