10.3 Heat Capacity

• At one time it was believed that an object contained a certain amount of “heat fluid” or “caloric” that could flow from one place to another.

• Experiments later revealed that heat (the transfer of thermal energy) was another form of energy. As such, it must be taken into account when applying the conservation of energy.

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Heat Capacity

• The equivalence between heat and work was first explored by James Prescott Joule.

• In an experiment using a device such as the one shown in the figure below, Joule demonstrated that the work done by gravity on falling masses resulted in the slight warming of water.

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Heat Capacity

© 2014 Pearson Education, Inc.

Heat Capacity • By measuring the mechanical work and the increase in

the water’s temperature, Joule was able to show that energy was conserved.

• Joule’s experiment established the mechanical equivalent of heat.

• The mechanical equivalent of heat is the precise amount of mechanical work that has the same effect as the transfer of a given amount of thermal energy. The relationship is as follows:

1 cal = 4.186 J 1 kcal = 4186 J

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Heat Capacity

• The customary unit for measuring heat is the calorie (cal). One kilocalorie (kcal) is defined as the amount of heat needed to raise the temperature of 1 kilogram of water from 14.5 °C to 15.5 °C.

• In nutrition, the Calorie (C) is used. Spelled with a capital C, one nutritional calorie (1 C) is the same as one kilocalorie.

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Heat Capacity

• The symbol Q is used to denote heat. • Heat may be expressed in joules or calories,

whichever is more convenient for a particular problem.

• Heat is positive when thermal energy is added to a system and negative when thermal energy is removed from a system.

© 2014 Pearson Education, Inc.

© 2014 Pearson Education, Inc.

Follow up Practice problems

1. How many calories are burned when the person of mass 70 kg climbs 100 stairs? Assume metabolic efficiency of 100%

2. During a workout, a person repeatedly lifts a 6.2 kg barbell through a distance of 0.58 m. How many reps of this lift are required to burn off 150 C?

Heat Capacity • The specific heat capacity of a substance is the

thermal energy required to change the temperature of 1 kilogram of the substance by 1 °C.

• Different substances require different amounts of thermal energy for the same change in temperature and therefore have different heat capacities.

• A substance with a high specific heat capacity requires a lot of thermal energy to show a given change in temperature.

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Heat Capacity • A useful analogy for specific heat capacity is

provided by the vases shown below. A vase with a large capacity for water is like a substance with a large capacity for thermal energy.

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Heat Capacity

• The specific heat capacity, designated with the symbol c, is defined as follows:

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Heat Capacity • The specific heat

capacities for some common substances are listed in the table below.

• Water’s unusually high specific heat capacity accounts for the nearly constant temperatures experienced in regions near large bodies of water.

© 2014 Pearson Education, Inc.

© 2014 Pearson Education, Inc.

1. Suppose 79.3 J of thermal energy is added to 111-g piece of aluminium at 22.5ºC. What is the final temperature of aluminium? c=900 J/(kg.K)

2. How much thermal energy is required to raise the temperature of a 55-g glass ball by 15⁰C?

Heat Capacity • A lightweight, insulated flask called a calorimeter is

used to measure specific heat capacity. Calorimetry is a practical application of energy conservation.

• A heated block of metal of known mass but unknown specific heat capacity is lowered into a calorimeter containing water of known mass and temperature.

• After equilibrium has been reached, the final temperature of the block-water system is measured.

• The specific heat is then determined by equating the thermal energy lost by the block to the thermal energy gained by the water.

© 2014 Pearson Education, Inc.

© 2014 Pearson Education, Inc.

© 2014 Pearson Education, Inc.

© 2014 Pearson Education, Inc.

1. What is the final equilibrium temperature if the mass of water in the calorimeter is decreased to 0.5 kg (the same as the mass of the block)?

2. A 235g lead ball at a temperature of 84.2⁰C is placed in a light calorimeter containing 177 g of water at 21.5⁰C. Find the equilibrium temperature of the system.

Follow up Practice problems

Review An 825-g iron block is heated to 352 ⁰C and placed in a container that absorbs a negligible amount of thermal energy and hold 40.0 g of water at 20.0 ⁰C. What is the equilibrium temperature of the system? Take the average specific heat capacity of iron as 560 J/(kg.⁰C) and for water 4186 J/(kg.⁰C)

QN: To determine the specific heat capacity of an object, a student heats it to 100 ⁰C in boiling water.She then places the 38-g object in 155-g aluminium calorimeter containing 103 g of water. The aluminium and water are initially at a temperature of 20.0 ⁰C and are thermally insulated from the surroundings. If the final temperature is 22.0 ⁰C, what is the specific heat capacity of the object?

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