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 per Kelvin (J/mol K). (b) The units of specific heat are Joules per gram per Kelvin (J/g K). (c) To calculate the heat capacity of a particular piece of copper pipe, we need to know its mass, in addition to the specific heat of copper.

Step 1: (a) Determine the units of molar heat capacity

Molar heat capacity is defined as the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius or Kelvin. The formula for molar heat capacity (C) is: C = q / (n * ΔT) Where: - C is the molar heat capacity - q is the heat absorbed or released by the substance - n is the number of moles of the substance - ΔT is the change in temperature (in Celsius or Kelvin) From the formula, we can determine the units of molar heat capacity. The unit of heat (q) is Joules (J), the unit of the number of moles (n) is moles (mol), and the unit of temperature change (ΔT) is either Celsius (°C) or Kelvin (K). To get the units for C, we divide the units of heat by the product of the units of the number of moles and the change in temperature: Units of C = (units of q) / (units of n * units of ΔT) = J / (mol * K) So, the units of molar heat capacity are Joules per mole per Kelvin (J/mol K).

Step 2: (b) Determine the units of specific heat

Specific heat is defined as the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius or Kelvin. The formula for specific heat (c) is: c = q / (m * ΔT) Where: - c is the specific heat - q is the heat absorbed or released by the substance - m is the mass of the substance (in grams) - ΔT is the change in temperature (in Celsius or Kelvin) To get the units for specific heat, we divide the units of heat by the product of the units of mass and the change in temperature: Units of c = (units of q) / (units of m * units of ΔT) = J / (g * K) So, the units of specific heat are Joules per gram per Kelvin (J/g K).

Step 3: (c) Additional information needed to calculate heat capacity

In order to calculate the heat capacity of a particular piece of copper pipe, we need to know both its mass and the specific heat of copper. The specific heat of copper is given in the problem. The formula to calculate the heat capacity (Q) is: Q = m * c * ΔT Where: - Q is the heat capacity - m is the mass of the copper pipe (in grams)

Key Concepts

Understanding Specific Heat

Specific heat is an important property that measures how much heat is needed to change the temperature of a substance. Specifically, it refers to the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius or Kelvin.
This concept is crucial in understanding how different materials respond to heat.

• Formula: The formula for specific heat (\( c \)) is \( c = \frac{q}{m \times \Delta T} \), where \( q \) is the heat absorbed or released, \( m \) is the mass in grams, and \( \Delta T \) is the change in temperature.
• Units: The units of specific heat are Joules per gram per Kelvin (J/g K).
• Significance: Understanding specific heat helps in determining how much energy is needed for heating or cooling substances during chemical reactions and physical processes.

Specific heat is a foundational concept in thermodynamics, aiding in tasks ranging from cooking to industrial applications.

Exploring Heat Capacity

Heat capacity is another fundamental concept that plays a key role in thermodynamics.
It refers to the total amount of heat required to change the temperature of an entire object or system by one degree Celsius or Kelvin.

• Formula: Heat capacity (\( Q \)) is calculated using the formula \( Q = m \times c \times \Delta T \), which combines mass, specific heat, and temperature change.
• Importance: Heat capacity helps understand how different objects, such as metals or fluids, store and release heat.

When you know the specific heat of a material, like copper, and you have its mass, you can determine the heat capacity of an object made from that material.
This is essential for both scientific calculations and practical applications, such as designing thermal systems.

Grasping Units of Measurement

Units of measurement are crucial in understanding and performing calculations in thermodynamics.
Each property, like specific heat or molar heat capacity, has its own units that convey how the substance behaves under thermal conditions.

• Molar Heat Capacity: Typically expressed in Joules per mole per Kelvin (J/mol K), this unit measures heat capacity per mole of a substance.
• Specific Heat: Expressed in Joules per gram per Kelvin (J/g K), these units measure the specific heat capacity of a substance.
• Why Units Matter: They ensure consistency and accuracy in scientific communications and calculations, allowing for precise conversions and predictions.

Understanding these units helps in deciphering equations and conversions, alongside ensuring the reliability of experimental and industrial outcomes.