Calorimetry with Temperature and Phase Changes Practice Problems

A mixture of 0.225 kg of ice and 1.20 kg of water in a thermally insulating tank has a temperature of 0.0 °C. Waste steam at 100°C exhausted from a cooking pot is conveyed into the tank. Determine the mass of steam that must be delivered in the tank to generate water at 50.0 °C. Assume that the tank absorbs negligible heat and that all processes occur at atmospheric pressure.

A 1 kg iron fajita sizzling plate with a temperature of 250.0 °C is removed from the oven. A big ice cube at 0 °C is placed on the plate. How much ice melts if we assume that all the heat released by the iron plate is transferred to the block of ice?

A mass of 0.300 kg of water at 60.0° C is placed in a massless thermos bottle.  How many grams of ice cubes, at a temperature of -10.0°C, must be poured into the water to get the system's final temperature to 30.0°C?

Hikers consume snow after it warms up. Suppose you consume 2.0 kg of snow at -10°C, and your body warms to 38°C. Calculate how much energy is absorbed from your body. Assume the specific heat of ice is 2100 J/kg⋅^∘C, the latent heat of fusion is 3.33×10⁵ J/kg⋅^∘C, Specific heat of liquid is 4186 J/kg⋅^∘C.

Determine the amount of heat necessary to convert a 15.7 kg solid block of iron at 20.0°C into a liquid at its melting point temperature. [Hint: The specific heat of iron is 4.50 × 10² J/kg.C° its latent heat of fusion is 289 kJ/kg, and its melting point temperature is 1540°C.]

A 56-g metal sphere traveling at 260 m/s penetrates a block of snow at its melting point (0°C) and comes to rest within the snow. How much snow is melted as a result of the collision if the temperature of the sphere doesn’t change significantly? Use fusion latent heat 333×10³ J/kg.

A flask containing liquid nitrogen is supplied with 4.50 x 10⁵ J of energy at -196°C. Calculate the amount of nitrogen that would evaporate. [Hint: Assume that the boiling point of nitrogen is -196°C and its latent heat of vaporization is 2.00 × 10⁵ J/kg.]

During a controlled test, an engineer observes that a 7.2-g copper bullet is able to strike a steel plate completely and notices that the bullet will melt at the point of impact with this plate during the collision event. The engineer is aiming to determine what the bullet's minimum initial velocity will be, given that bullet is fired at room temperature of 30°C. Let us also assume that the fusion latent heat of copper is L=2.07×10⁵ J/kg.

A 190 kg copper kettle (specific heat capacity: 390 J/kg·°C) is initially filled with 720 kg of milk at 19°C. If a burner provides energy at a rate of 59,000 kJ/h, how long will it take the milk reach its boiling point? (Assume the specific heat capacity of milk is similar to that of water: 4186 J/kg·°C).

The water in a kettle has been boiling (at 100°C) for 10 mins. In total, 220 kcal of heat has been provided to the kettle in the meantime. Calculate the amount of water that is vaporized. [Hint: The latent heat of vaporization of water = 540 kcal/kg].

A copper fragment heats up and melts as it enters the atmosphere of Venus. What minimum velocity must the fragment have had before entering the Venusian atmosphere if its initial temperature was -110°C? Assume the melting point of copper is 1100°C, the specific heat capacity of copper is 390 J/kg·°C, and the latent heat of fusion of copper is 2.1 × 10⁵ J/kg.

A piece of ice weighing around 40 g just started melting when it got dropped into an insulated container filled with liquid Argon which was kept at boiling temperature, i.e., 87 K. The latent heat of vaporization for Argon is given as 160 kJ/Kg, find out how much Argon would have evaporated. Assume that the specific heat capacity of ice is 2100 J/kgC.

A steel mill experiences a malfunction, causing molten steel to spill and create a 15.0-meter-wide, 18.0 centimeter-thick stream. The stream of molten steel is advancing at a rate of 0.70 meters per minute and has a scorching temperature of 1610°C. To rectify the situation, the mill supervisor uses water (22°C) to rapidly cool and solidify the metal. Given the steel's properties, such as a density of 7850 kg/m³, specific heat of 500 J/kg K, solidification temperature of 1500°C, and heat of fusion of 2.00×10⁵ J/kg, calculate the flow rate, in liters per minute, required to halt the flow of molten steel.

A slaughterhouse preserves meat for a few weeks by keeping it at low temperatures below 5°C. Suppose meat (at 37°C) is cooled until its internal temperature is 2.0°C using an ice-water mixture. Determine the least amount of ice at 0°C required to cool 65.0 kg of meat so that the temperature of the bath is maintained at 0°C. Meat has a specific heat of 3480 J/kg°C.

In an experiment, a student releases 10 pieces of one-dollar coins heated to 140 °C into a thermally insulating container of mass 50 g and specific heat capacity 420 J/kg•°C. The container is filled with a mixture of ice (5 g) and water (200 g) at the same temperature. Each coin has a specific heat of 390 J/kg•°C and a mass of 8.1 g. Determine the final temperature (T). Assume that the container does not allow heat exchange with surroundings.

A 500 g block of aluminum is heated to 400 ℃ and dropped into water initially at 20 ℃. What is the minimum mass of water (m_w) required to cool down the block to 125 ℃?