The heat Q that must be supplied or removed to change the temperature of a substance of mass m by an amount ∆T is:

Q = cm∆Twhere c is the specific heat capacity of the substance.

The common unit for specific heat capacity is the J/(kg•C°). The value of specific heat capacity depends on the nature of the material.

Ex. 9 - In a half hour, a 65-kg jogger can generate 8.0 x 105 J of heat. This heat is removed from the jogger’s body by a variety of means. If the heat were not removed, how much would the body temperature increase? c for the human body = 3500 J/(kg•C°).

Other than the joule; the calorie, kilocalorie and the British thermal unit are common heat units. c for water is 1.00 kcal/(kg•C°) or 1.00 cal/(g•C°).

James Joule (1818-1889) showed that work energy and heat energy were related. He showed that 1 kcal = 4186 joules or 1 cal = 4.186 joules.

1 kcal = 4186 joules or 1 cal = 4.186 joules.

This conversion factor is the mechanical equivalent of heat.

Ex. 10 - Cold water at 15 °C enters a heater, and the resulting hot water has a temperature of 61°C. A person uses 120 kg of hot water in taking a shower. (a) Find the energy needed to heat the water. (b) Assuming that the power utility charges $0.10 per kilowatt•hour for electrical energy, determine the cost of heating the water.

The value of specific heat capacity depends on whether pressure or volume are held constant. This distinction is usually not important for liquids and solids but is significant for gases.

A calorimeter is an insulated container which can be used to measure heat loss or gain between materials contained within.

Ex.11 - A calorimeter cup is made from 0.15 kg of aluminum and contains 0.20 kg of water. Initially, the water and the cup have a common temp. of 18.0 °C. An unknown material (m = 0.040 kg) is heated to a temperature of 97.0 °C and then added to the water. The temp. of the water, cup, and unknown is 22.0 °C after thermal equilibrium. Find the specific heat capacity of the unknown material.

Ex.12 - Suppose you are cooking spaghetti for dinner, and the instructions say to boil the noodles in water fro ten minutes. To cook spaghetti in an open pot with the least amount of energy, should you turn up the burner to its fullest so the water vigorously boils, or should you turn down the burner so the water barely boils?

The latent heat is the heat per kilogram that must be added or removed when a substance changes from one phase to another at a constant temperature. The unit is the J/kg.

The latent heat of fusion Lf refers to a solid to liquid change. The latent heat of vaporization Lv refers to a liquid to gas change.The latent heat of sublimation Ls refers to a solid to gas change.

Ex.13 - Ice at 0°C is placed in a Styrofoam cup containing 0.32 kg of lemonade at 27°C. The specific heat capacity of lemonade is virtually the same as water. After the ice and lemonade reach equilibrium, some ice still remains. Determine the mass of ice that has melted.

Ex.14 - A 7.00-kg glass bowl [c = 840 J/(kg•C°)] contains 16.0 kg of punch at 25.0 °C. Two-and-a-half kg of ice [c = 200 J/(kg•C°)] are added to the punch. The ice has an initial temp. of -20.0 °C. The punch may be treated as if it were water [c = 4186 J/(kg•C°)]. When thermal equilibrium is reached, all the ice has melted, and the final temperature is above 0 °C. Determine this temperature.

Under specific conditions, a substance can exist in equilibrium in more than one phase at the same time. If a liquid partially fills a vacuum, some of the molecules at the surface will escape the liquid and form a vapor; the vapor gathers heat for this change from collisions with other molecules.

As the number of vapor molecules increases, more and more return to the liquid state. Eventually, the number returning to the liquid state equals the number changing to the vapor state. From this time on, the concentration of vapor does not change, and the pressure due to this vapor remains constant.

The pressure of the vapor that coexists in equilibrium with the liquid is the equilibrium vapor pressure of the liquid.

Equilibrium vapor pressure does not depend on the volume of space available; it depends only on the temperature of the liquid; a higher temperature results in a higher pressure.

A graph of the equilibrium pressure vs. the equilibrium temperature can be plotted and the resulting curve is the vapor pressure curve, or the vaporization curve.

If water is boiled in an open container, the pressure of the water vapor must equal the air pressure (1.01 x 105 Pa). On the vaporization curve of water, this pressure corresponds to a temperature of 100°C.

A liquid boils at the temperature for which its vapor pressure equals the external pressure.Therefore, the boiling point of water is lower for lower pressures and higher for higher pressures.

A solid can also be in equilibrium with its liquid phase only at certain specific conditions of temperature and pressure. For each temperature, there is a single pressure at which solid and liquid can exist.

A plot of equilibrium pressure vs. equilibrium temperature for solid and liquid is called a fusion curve.

The total pressure of a mixture of gases, such as air, is the sum of the partial pressures of the component gases.

The partial pressure of a gas is the pressure it would exert if it alone occupied the entire volume at the same temperature as the mixture.

Relative humidity is the ratio of the partial pressure of water vapor in the air to the equilibrium vapor pressure at a given temperature.

Percent relative humidity is equal to the partial pressure of water vapor divided by the equilibrium vapor pressure of water at the existing temperature multiplied by 100.

The vapor pressure in the air cannot exceed the value in the denominator; if it did, it would condense as dew or rain.

When the partial pressure equals the equilibrium vapor pressure, the relative humidity is 100%. The vapor is said to be saturated.

If air containing water vapor is cooled, a temperature is reached where partial pressure is equal to equilibrium vapor pressure. This is called the dew point and would correspond to a relative humidity of 100%.

The dew point is the temperature below which water vapor in the air will condense into dew or fog. Water forms on the outside of a glass when the temperature of the air around the glass cools to below the dew point.