Problem 49 - Chemistry The Central Science

Question

(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?

Step-by-Step Solution

Answer

(a) The units of molar heat capacity are joules per mole degree Celsius (or Kelvin), written as J/(mol·K). (b) The units of specific heat are joules per gram degree Celsius (or Kelvin), written as J/(g·K) or joules per kilogram degree Celsius (or Kelvin), written as J/(kg·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 = mcΔT, we can then determine the heat capacity.

Step 1: (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·K).

Step 2: (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·K) or joules per kilogram degree Celsius (or Kelvin), written as J/(kg·K).

Step 3: (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 = mcΔT, where Q is the heat capacity, m is the mass, c is the specific heat, and ΔT 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 = mcΔT.