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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

Under constant-volume conditions, the heat of combustion of benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\) is \(26.38 \mathrm{~kJ} / \mathrm{g}\). A 2.760 -g sample of benzoic acid is burned in a bomb calorimeter. The temperature of the calorimeter increases from \(21.60^{\circ} \mathrm{C}\) to \(29.93^{\circ} \mathrm{C}\). (a) What is the total heat capacity of the calorimeter? (b) \(\mathrm{A}\) 1.440-g sample of a new organic substance is combusted in the same calorimeter. The temperature of the calorimeter increases from \(22.14^{\circ} \mathrm{C}\) to \(27.09^{\circ} \mathrm{C}\). What is the heat of combustion per gram of the new substance? (c) Suppose that in changing samples, a portion of the water in the calorimeter were lost. In what way, if any, would this change the heat capacity of the calorimeter?

When a \(6.50-\mathrm{g}\) sample of solid sodium hydroxide dissolves in \(100.0 \mathrm{~g}\) of water in a coffee-cup calorimeter (Figure 5.18 ), the temperature rises from \(21.6^{\circ} \mathrm{C}\) to \(37.8^{\circ} \mathrm{C}\). Calculate \(\Delta H\) (in \(\mathrm{kJ} / \mathrm{mol} \mathrm{NaOH})\) for the solution process $$ \mathrm{NaOH}(s) \longrightarrow \mathrm{Na}^{+}(a q)+\mathrm{OH}^{-}(a q) $$ Assume that the specific heat of the solution is the same as that of pure water.

Under constant-volume conditions, the heat of combustion of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) is \(15.57 \mathrm{~kJ} / \mathrm{g}\). A 3.500 -g sample of glucose is burned in a bomb calorimeter. The temperature of the calorimeter increased from \(20.94^{\circ} \mathrm{C}\) to \(24.72^{\circ} \mathrm{C}\). (a) What is the total heat capacity of the calorimeter? (b) If the size of the glucose sample had been exactly twice as large, what would the temperature change of the calorimeter have been?

What is the connection between Hess's law and the fact that \(H\) is a state function?

The specific heat of octane, \(\mathrm{C}_{8} \mathrm{H}_{18}(l),\) is \(2.22 \mathrm{~J} / \mathrm{g}-\mathrm{K}\). (a) How many J of heat are needed to raise the temperature of \(80.0 \mathrm{~g}\) of octane from \(10.0{ }^{\circ} \mathrm{C}\) to \(25.0{ }^{\circ} \mathrm{C} ?\) (b) Which will require more heat, increasing the temperature of \(1 \mathrm{~mol}\) of \(\mathrm{C}_{8} \mathrm{H}_{18}(l)\) by a certain amount or increasing the temperature of \(1 \mathrm{~mol}\) of \(\mathrm{H}_{2} \mathrm{O}(l)\) by the same amount?
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