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 \(\frac{Joules}{mole \cdot °C}\). (b) The units of specific heat are \(\frac{Joules}{gram \cdot °C}\). (c) To calculate the heat capacity of a particular piece of copper pipe, given the specific heat of copper, we need the mass of the copper pipe. The heat capacity can be calculated using the formula: Heat Capacity = Specific Heat × Mass.

Step 1: Find the units of molar heat capacity.

Molar heat capacity is the amount of heat required to raise the temperature of 1 mole of a substance by 1 degree Celsius. The unit of heat is Joule (J), temperature is measured in Celsius (°C), and the amount of substance is measured in moles (mol). Therefore, the units of molar heat capacity are \(\frac{Joules}{mole \cdot °C}\).

Step 2: Find the units of specific heat.

Specific heat is the amount of heat required to raise the temperature of 1 gram of a substance by 1 degree Celsius. The unit of heat is Joule (J), temperature is measured in Celsius (°C), and mass is measured in grams (g). Therefore, the units of specific heat are \(\frac{Joules}{gram \cdot °C}\).

Step 3: Identify additional information needed to calculate heat capacity.

If we know the specific heat of copper, to calculate the heat capacity of a particular piece of copper pipe, we also need to know the mass of the copper pipe. Heat capacity is the product of specific heat and mass, so with both of these pieces of information, the heat capacity can be calculated using the following formula: Heat Capacity = Specific Heat × Mass Hence, the additional information needed is the mass of the copper pipe.