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?

Short answer

(a) The units of molar heat capacity are \(\frac{J}{mol \cdot K}\). (b) The units of specific heat are \(\frac{J}{kg \cdot K}\). (c) To calculate the heat capacity of a particular piece of copper pipe when its specific heat is known, we need an additional piece of information: the mass of the copper pipe. With the mass, we can use the formula \(Heat \, Capacity (Q) = Specific \, Heat (c) \cdot Mass (m)\) to calculate the heat capacity.

Step-by-step solution

(a) Units of Molar Heat Capacity

Molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius (or kelvin). Its units are determined by dividing heat quantity by the temperature change and the amount of the substance present in moles. In SI units, the heat quantity is measured in J (joules), temperature change in °C or K (degrees Celsius or Kelvin), and the amount of substance in mol (moles). Thus, the units of molar heat capacity are given by: \[ \frac{J}{mol \cdot K} \]

(b) Units of Specific Heat

Specific heat capacity, or simply specific heat, is defined as the amount of heat required to raise the temperature of one unit mass of a substance by one degree Celsius or Kelvin. It's given by the heat quantity divided by the product of the mass and temperature change. In SI units, the heat quantity is measured in J (joules), temperature change in °C or K (degrees Celsius or Kelvin), and mass in kg (kilograms). Therefore, the units of specific heat are given by: \[ \frac{J}{kg \cdot K} \]

(c) Additional Information for Heat Capacity Calculation of a Copper Pipe

To calculate the heat capacity of a particular piece of copper pipe, when its specific heat is known, we need to know the mass of the copper pipe. Heat capacity is the product of specific heat and mass: \[ Heat \, Capacity (Q) = Specific \, Heat (c) \cdot Mass (m) \] With the mass of the copper pipe, we can calculate the heat capacity (Q) by multiplying the specific heat (c) of copper with the mass (m) of the copper pipe.