Intro to Calorimetry Practice Problems

You are preparing water for dishwashing at home. You place 4.50 kg of water whose temperature is 8.0°C in an insulated pale. The desired final temperature of the water is 61°C. Determine the quantity of boiling water (100.0°C) that will heat the water to the desired temperature.

A blacksmith places a 390-gram iron horseshoe inside a tank that contains 5.0 liters of water at 298 K. A thermometer shows a fast increase in the water temperature, reaching a value of 301 K. Determine the original temperature in degrees Celsius and Fahrenheit of the horseshoe before it was immersed in water.

A 0.120-kg copper calorimeter cup containing 0.200 kg of oil and a 0.0250-kg plastic stirrer at 15.0°C has a 0.150-kg metal rod heated to 4.00 × 10² °C plunged into it. The final temperature of the system reaches 45.0 °C. Given that the specific heat of copper is 385 J/kg^.°C, the specific heat of the oil is 3540 J/kg^.°C, and the specific heat of the plastic stirrer is 1780 J/kg^.°C, determine the specific heat of the metal rod. Assume no oil evaporates.

A scientist extracts 220 grams of aluminum nuggets from a furnace heated to 400°C and quickly places them into 150 mL of water at 15°C within a thermally insulated container. Determine the resulting equilibrium temperature of the water after the aluminum nuggets are added.

An adventurer collects a 600 g sample of an enigmatic metal with an initial temperature of 8°C. The adventurer immerses the metal in a 120 g  copper vessel filled with 420 g of water at 95°C. After a while, the temperature of the water, metal, and vessel reaches equilibrium at 75°C. Identify the metal in the sample.

A geothermal power plant harnesses underground heat to generate 1450 MW (1450 MJ/s) of electric energy. During the process, 4110 MW of excess heat needs to be dissipated to maintain operational safety. To cool the system, the plant pumps water from a nearby river. When the water enters the cooling mechanism, it has an initial temperature of 20°C. To protect the local aquatic life, regulations state that the water temperature cannot exceed 35°C upon returning to the river. Calculate the flow rate of river water, in L/min, required to maintain the power plant's safe and efficient operation.

Determine the initial temperature of iron when 15 g of brass at 250°C and 25 g of iron are placed into 75 cm³ of isopropyl alcohol initially at 10°C. The mixture's temperature eventually stabilizes at 30°C. Consider the following specific heat capacities: iron 450 J/(kg•K), brass 380 J/(kg•K), isopropyl alcohol  2440 J/(kg•K); and a density of 786 kg/m³ for isopropyl alcohol.

The temperature of water in a Styrofoam cup increases from 30 °C to 33 °C when a 10 g cylinder of unknown metal at 430 °C is dropped in the water. The mass of the water is 250 g. The mass of the Styrofoam cup is 8.1 g, and its specific heat capacity is 1131 J/kg•K. Assume that the cup is a perfect thermal insulator. Calculate the specific heat capacity of the unknown metal (c_metal).

Suppose you mix 200 g of water at 80°C with 100 ml of ethanol at 20°C. What will be the final temperature of the mixture if the specific heat of water is 4.18 J/g°C and that of ethanol is 2.44 J/g°C? Assume that there is no heat loss to the surroundings and the ethanol does not evaporate. The density of ethanol is 789 kg/m³.

A student put 100 g of metal heated to 150 °C, in a 250 g copper calorimeter filled with 250 g of water. The initial temperature of the calorimeter and water is 30 °C. What would the final temperature (T_f) of the system be if the metal's specific heat capacity was 498 J/kg•°C? Assume that there is no heat transferred to the environment.