Advanced Calorimetry: Equilibrium Temperature with Phase Changes Practice Problems

Find the final result of mixing ice cubes at 0°C with 100°C water vapors in a container if both have the same mass. Use the following latent heat coefficients for the ice melting which is 333 ×10³ J/kg, that the water vapors during condensation is 2260 kJ/kg, and that specific heat coefficients for the water is 4.186 kJ/(kg$\cdot$°C).

Scientists are experimenting with ethanol. In an isolated container, they put 2.00 kg of solid ethanol at -114°C (the melting point of ethanol) and some amount of ethanol in its gaseous form at a temperature of 78.4°C (boiling point of ethanol). As a result, all the ethanol turned into its liquid form at 10.0°C. Calculate the amount of gaseous ethanol that was initially put in the container with its liquid form.

[Hint: The latent heat of the vaporization of ethanol is 8.54 × 10⁵ J / kg, its latent heat of fusion is 1.08 × 10⁵ J / kg and the specific heat of liquid ethanol is 2440 J/kg·°C]

A 1.52 kg block of gallium being stored at its melting point temperature of 30.0°C is kept in an iron container of mass 0.430 kg. The container contains 0.510 kg of water. Given that, the initial temperature of the container and water is 90.5°C and the final temperature of the system is 36.6°C. Calculate what the latent heat of fusion of gallium will be.

[Hint: The specific heat capabilities of gallium, iron, and water are respectively 370 J/kg°C, 450 J/kg°C, and 4180 J/kg°C]

In an insulated container of negligible mass, a 4.00-kg piece of iron at an unknown initial temperature is placed with 3.00 kg of ice at -30.0°C. After reaching thermal equilibrium, the container holds 2.20 kg of ice and 0.80 kg of liquid water. Determine the initial temperature of the iron. Use the Specific heat capacity of ice, 𝑐_𝑖=2.1J/g°C, the Specific heat capacity of iron, 𝑐_Fe=0.45 J/g°C, Latent heat of fusion of ice, 𝐿_𝑓=334 J/g.

A science experiment involves a student with a mass of approximately 75.0 kg and a body temperature of about 38.0 °C drinking half a liter of water at 8.00 °C at the beginning. What will his new body temperature be after reaching thermal equilibrium? Assume that there's no metabolic heating during this period. The specific heat capacity for human bodies is typically around 3480 J/kg⋅K. The specific heat capacity of water is 4186 J/kg⋅K.

In a laboratory experiment, a researcher takes a cube of ammonia from a freezer set to -100.0°C and places it into a 100 g silver calorimeter containing 500 g of water. The water is initially at room temperature, 25.0°C. After some time, the system reaches thermal equilibrium, with all the water at 10.0°C. Given this information, determine the mass of the ammonia cube used in the experiment. Use specific heat capacity of ammonia (solid) = 2.09 J/g^.°C, specific heat capacity of ammonia (liquid) = 4.70 J/g^.°C, specific heat capacity of silver = 0.235 J/g^.°C, specific heat capacity of water = 4.18 J/g^.°C, and heat of fusion of ammonia = 332 J/g.

A 400 g piece of copper initially at a temperature of 500°C is placed in 300 g water at 60.0°C. Calculate the mass of water that boils away.