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Chapter 5: Problem 49

(a) What are the units of molar heat capacity? (b) What are the units of specific heat? (c) If you know the specific heat of copper, what additional information do you need to calculate the heat capacity of a particular piece of copper pipe?

Short Answer

Expert verified
(a) The units of molar heat capacity are joules per mole degree Celsius (or Kelvin), written as J/(mol路K). (b) The units of specific heat are joules per gram degree Celsius (or Kelvin), written as J/(g路K) or joules per kilogram degree Celsius (or Kelvin), written as J/(kg路K). (c) To calculate the heat capacity of a particular piece of copper pipe, we need the mass of the copper pipe and the specific heat of copper. Using the formula Q = mc螖T, we can then determine the heat capacity.

Step by step solution

01

(a) Units of Molar Heat Capacity

Molar heat capacity is defined as the amount of heat needed to raise the temperature of one mole of a substance by one degree Celsius (or one Kelvin). The units of molar heat capacity can be obtained by considering its definition. Heat is usually measured in joules (J), and the amount of substance is measured in moles (mol). Therefore, the units of molar heat capacity are joules per mole degree Celsius (or Kelvin), written as J/(mol路K).
02

(b) Units of Specific Heat

Specific heat is defined as the amount of heat needed to raise the temperature of one unit mass of a substance by one degree Celsius (or one Kelvin). Similar to molar heat capacity, the units of specific heat can be obtained by considering its definition. Heat is measured in joules (J), and the mass is measured in grams (g) or kilograms (kg). Therefore, the units of specific heat are joules per gram degree Celsius (or Kelvin), written as J/(g路K) or joules per kilogram degree Celsius (or Kelvin), written as J/(kg路K).
03

(c) Additional Information Required

To calculate the heat capacity of a particular piece of copper pipe, we need the following additional information: 1. The mass of the copper pipe: Mass is needed to calculate the heat capacity because heat capacity is related to the specific heat and mass. The heat capacity formula can be written as Q = mc螖T, where Q is the heat capacity, m is the mass, c is the specific heat, and 螖T is the change in temperature. 2. The specific heat of copper (which is given): This value is necessary to perform the calculation using the formula mentioned above. Once we have the mass of the copper pipe and the specific heat of copper, we can calculate the heat capacity of the copper pipe using the formula Q = mc螖T.

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Most popular questions from this chapter

The automobile fuel called E85 consists of \(85 \%\) ethanol and \(15 \%\) gasoline. \(\mathrm{E} 85\) can be used in so-called "flex-fuel" vehicles (FFVs), which can use gasoline, ethanol, or a mix as fuels. Assume that gasoline consists of a mixture of octanes (different isomers of \(\mathrm{C}_{8} \mathrm{H}_{18}\) ), that the average heat of combustion of \(\mathrm{C}_{8} \mathrm{H}_{18}(l)\) is \(5400 \mathrm{~kJ} / \mathrm{mol}\), and that gasoline has an average density of \(0.70 \mathrm{~g} / \mathrm{mL}\). The density of ethanol is \(0.79 \mathrm{~g} / \mathrm{mL}\). (a) By using the information given as well as data in Appendix C, compare the energy produced by combustion of \(1.0 \mathrm{~L}\) of gasoline and of \(1.0 \mathrm{~L}\) of ethanol. (b) Assume that the density and heat of combustion of \(\mathrm{E} 85\) can be obtained by using \(85 \%\) of the values for ethanol and \(15 \%\) of the values for gasoline. How much energy could be released by the combustion of \(1.0 \mathrm{~L}\) of E85? (c) How many gallons of E85 would be needed to provide the same energy as 10 gal of gasoline? (d) If gasoline costs \(\$ 3.10\) per gallon in the United States, what is the break-even price per gallon of \(\mathrm{E} 85\) if the same amount of energy is to be delivered?

(a) A baseball weighs 5.13 oz. What is the kinetic energy in joules of this baseball when it is thrown by a major-league pitcher at \(95.0 \mathrm{mph}\) ? (b) By what factor will the kinetic energy change if the speed of the baseball is decreased to \(55.0 \mathrm{mph} ?\) (c) What happens to the kinetic energy when the baseball is caught by the catcher? (d) What careful experimental measurement could (in principle) be made to confirm your answer to (c)?

The gas-phase reaction shown, between \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\), was run in an apparatus designed to maintain a constant pressure. (a) Write a balanced chemical equation for the reaction depicted and predict whether \(w\) is positive, negative, or zero. (b) Using data from Appendix \(\mathrm{C}\), determine \(\Delta H\) for the formation of one mole of the product. Why is this enthalpy change called the enthalpy of formation of the involved product? [Sections 5.3 and 5.7\(]\)

For each of the following compounds, write a balanced thermochemical equation depicting the formation of one mole of the compound from its elements in their standard states and use Appendix \(\mathrm{C}\) to obtain the value of \(\Delta H_{f}^{\circ}\) : (a) \(\mathrm{NO}_{2}(g)\) (b) \(\mathrm{SO}_{3}(g),(\mathrm{c}) \mathrm{NaBr}(s)\) (d) \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(s)\)

(a) Calculate the kinetic energy in joules of a \(1200-\mathrm{kg}\) automobile moving at \(18 \mathrm{~m} / \mathrm{s}\). (b) Convert this energy to calories. (c) What happens to this energy when the automobile brakes to a stop?
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