20. Heat and Temperature

A copper calorimeter can with mass 0.100 kg contains 0.160 kg of water and 0.0180 kg of ice in thermal equilibrium at atmospheric pressure. If 0.750 kg of lead at 255°C is dropped into the calorimeter can, what is the final temperature? Assume that no heat is lost to the surroundings.

A vessel whose walls are thermally insulated contains $2.40$ kg of water and $0.450$ kg of ice, all at $0.0$°C. The outlet of a tube leading from a boiler in which water is boiling at atmospheric pressure is inserted into the water. How many grams of steam must condense inside the vessel (also at atmospheric pressure) to raise the temperature of the system to $28.0$°C? You can ignore the heat transferred to the container.

A $4.00$-kg silver ingot is taken from a furnace, where its temperature is $750.0$°C, and placed on a large block of ice at $0.0$°C. Assuming that all the heat given up by the silver is used to melt the ice, how much ice is melted?

An insulated beaker with negligible mass contains $0.250$ kg of water at $75.0$°C. How many kilograms of ice at $-20.0$°C must be dropped into the water to make the final temperature of the system $40.0$°C?

(II) High-altitude mountain climbers do not eat snow, but always melt it first with a stove. To see why, calculate the energy absorbed from your body if you eat 1.0 kg of -15°C snow which your body warms to body temperature of 37°C.

How much heat is needed to melt 26.50 kg of silver that is initially at 25°C?

If 3.40 x 10⁵ J of energy is supplied to a container of liquid oxygen at -183° C , how much oxygen can evaporate?

At a crime scene, the forensic investigator notes that the 6.2-g lead bullet that was stopped in a doorframe apparently melted completely on impact. Assuming the bullet was shot at room temperature (20°C), what does the investigator calculate as the minimum muzzle velocity of the gun?

An iron boiler of mass 180 kg contains 710 kg of water at 18°C. A heater supplies energy at the rate of 58,000 kJ/h. How long does it take for the water to reach the boiling point?

(II) During exercise, a person may give off 185 kcal of heat in 25 min by evaporation of water (at 20°C) from the skin. How much water has been lost? [Hint: See page 548.]

An iron meteorite melts when it enters the Earth’s atmosphere. If its initial temperature was -105° C outside of Earth’s atmosphere, calculate the minimum velocity the meteorite must have had before it entered Earth’s atmosphere.

(II) A 28-g ice cube at its melting point is dropped into an insulated container of liquid nitrogen. How much nitrogen evaporates if it is at its boiling point of 77 K and has a latent heat of vaporization of 200 kJ/kg? Assume for simplicity that the specific heat of ice is a constant and is equal to its value near its melting point.

A lava flow is threatening to engulf a small town. A 400-m-wide, 35-cm-thick tongue of 1200°C lava is advancing at the rate of 1.0 m per minute. The mayor devises a plan to stop the lava in its tracks by flying in large quantities of 20°C water and dousing it. The lava has density 2500 kg/m³, specific heat 1100 J/kg K, melting temperature 800°C, and heat of fusion 4.0×10⁵ J/kg. How many liters of water per minute, at a minimum, will be needed to save the town?

One suggested treatment for a person who has suffered a stroke is immersion in an ice-water bath at 0°C to lower the body temperature, which prevents damage to the brain. In one set of tests, patients were cooled until their internal temperature reached 32.0°C. To treat a 70.0 kg patient, what is the minimum amount of ice (at 0°C) you need in the bath so that its temperature remains at 0°C? The specific heat of the human body is 3480 J/kg C°, and recall that normal body temperature is 37.0°C.