Calculate the one temperature at which Fahrenheit and Celsius thermometers agree with each other.

Calculate the one temperature at which Fahrenheit and Kelvin thermometers agree with each other

The pressure of a gas at the triple point of water is $1.35$ atm. If its volume remains unchanged, what will its pressure be at the temperature at which CO₂ solidifies?

A constant-volume gas thermometer registers an absolute pressure corresponding to $325$ mm of mercury when in contact with water at the triple point. What pressure does it read when in contact with water at the normal boiling point?

Like the Kelvin scale, the Rankine scale is an absolute temperature scale: Absolute zero is zero degrees Rankine (0°R). However, the units of this scale are the same size as those of the Fahrenheit scale rather than the Celsius scale. What is the numerical value of the triple-point temperature of water on the Rankine scale?

One of the tallest buildings in the world is the Taipei 101 in Taiwan, at a height of 1671 feet. Assume that this height was measured on a cool spring day when the temperature was 15.5°C. You could use the building as a sort of giant thermometer on a hot summer day by carefully measuring its height. Suppose you do this and discover that the Taipei 101 is 0.471 foot taller than its official height. What is the temperature, assuming that the building is in thermal equilibrium with the air and that its entire frame is made of steel?

A geodesic dome constructed with an aluminum framework is a nearly perfect hemisphere; its diameter measures 55.0 m on a winter day at a temperature of -15°C. How much more interior space does the dome have in the summer, when the temperature is 35°C?

A 6.00-kg piece of solid copper metal at an initial temperature T is placed with 2.00 kg of ice that is initially at -20.0°C. The ice is in an insulated container of negligible mass and no heat is exchanged with the surroundings. After thermal equilibrium is reached, there is 1.20 kg of ice and 0.80 kg of liquid water. What was the initial temperature of the piece of copper?

A steel tank is completely filled with 1.90 m³ of ethanol when both the tank and the ethanol are at 32.0°C. When the tank and its contents have cooled to 18.0°C, what additional volume of ethanol can be put into the tank?

As a new mechanical engineer for Engines Inc., you have been assigned to design brass pistons to slide inside steel cylinders. The engines in which these pistons will be used will operate between 20.0°C and 150.0°C. Assume that the coefficients of expansion are constant over this temperature range. If the piston just fits inside the chamber at 20.0°C, will the engines be able to run at higher temperatures? Explain.

Steel train rails are laid in 12.0-m-long segments placed end to end. The rails are laid on a winter day when their temperature is -9.0°C. How much space must be left between adjacent rails if they are just to touch on a summer day when their temperature is 33.0°C?

A brass rod is 185 cm long and 1.60 cm in diameter. What force must be applied to each end of the rod to prevent it from contracting when it is cooled from 120.0°C to 10.0°C?

In an effort to stay awake for an all-night study session, a student makes a cup of coffee by first placing a 200-W electric immersion heater in 0.320 kg of water. How much time is required? Assume that all of the heater's power goes into heating the water.

In very cold weather a significant mechanism for heat loss by the human body is energy expended in warming the air taken into the lungs with each breath. On a cold winter day when the temperature is -20°C, what amount of heat is needed to warm to body temperature (37°C) the 0.50 L of air exchanged with each breath? Assume that the specific heat of air is 1020 J/kg K and that 1.0 L of air has mass 1.3 × 10^-3 kg.

While painting the top of an antenna 225 m in height, a worker accidentally lets a 1.00-L water bottle fall from his lunchbox. The bottle lands in some bushes at ground level and does not break. If a quantity of heat equal to the magnitude of the change in mechanical energy of the water goes into the water, what is its increase in temperature?

A nail driven into a board increases in temperature. If we assume that 60% of the kinetic energy delivered by a 1.80 kg hammer with a speed of 7.80 m/s is transformed into heat that flows into the nail and does not flow out, what is the temperature increase of an 8.00 g aluminum nail after it is struck ten times?

You have 750 g of water at 10.0°C in a large insulated beaker. How much boiling water at 100.0°C must you add to this beaker so that the final temperature of the mixture will be 75°C?

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.

A blacksmith cools a 1.20 kg chunk of iron, initially at 650.0°C, by trickling 15.0°C water over it. All of the water boils away, and the iron ends up at 120.0°C. How much water did the blacksmith trickle over the iron?

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 copper pot with a mass of 0.500 kg contains 0.170 kg of water, and both are at 20.0°C. A 0.250-kg block of iron at 85.0°C is dropped into the pot. Find the final temperature of the system, assuming no heat loss to the surroundings.

Before going in for his annual physical, a 70.0 kg man whose body temperature is 37.0°C consumes an entire 0.355-L can of a soft drink (mostly water) at 12.0°C. What will his body temperature be after equilibrium is attained? Ignore any heating by the man’s metabolism. The specific heat of the man’s body is 3480 J/kg K.

An ice-cube tray of negligible mass contains 0.290 kg of water at 18.0°C. How much heat must be removed to cool the water to 0.00°C and freeze it? Express your answer in joules, calories, and Btu.

An asteroid with a diameter of 10 km and a mass of 2.60 × 10¹⁵ kg impacts the earth at a speed of 32.0 km/s, landing in the Pacific Ocean. If 1.00% of the asteroid's kinetic energy goes to boiling the ocean water (assume an initial water temperature of 10.0°C), what mass of water will be boiled away by the collision? (For comparison, the mass of water contained in Lake Superior is about 2 × 10¹⁵ kg.)

A laboratory technician drops a $0.0850$-kg sample of unknown solid material, at $100.0$°C, into a calorimeter. The calorimeter can, initially at $19.0$°C, is made of $0.150$ kg of copper and contains $0.200$ kg of water. The final temperature of the calorimeter can and contents is $26.1$°C. Compute the specific heat of the sample.

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?

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?

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.

Two rods, one made of brass and the other made of copper, are joined end to end. The length of the brass section is $0.300$ m and the length of the copper section is $0.800$ m. Each segment has cross-sectional area $0.00500$ m². The free end of the brass segment is in boiling water and the free end of the copper segment is in an ice–water mixture, in both cases under normal atmospheric pressure. The sides of the rods are insulated so there is no heat loss to the surroundings. What mass of ice is melted in $5.00$ min by the heat conducted by the composite rod?

Suppose that the rod in Fig. $17.24$a is made of copper, is $45.0$ cm long, and has a cross-sectional area of $1.25$ cm² . Let $TH=100.0$°C and $TC=0.0$°C. What is the final steady-state temperature gradient along the rod?