7. Energy, Rate and Equilibrium

Heat Capacity

7. Energy, Rate and Equilibrium

Heat Capacity: Videos & Practice Problems

Topic summary

Heat capacity measures the heat required to change a substance's temperature, with specific heat capacity (c) defined as the heat needed to raise 1 gram by 1 degree Celsius or Kelvin, and molar heat capacity (C) for 1 mole. The equations are q=mcΔT for specific heat and C=q⁄nΔT for molar heat. Understanding these concepts is crucial for applications in thermodynamics and chemical reactions.

Heat Capacity is the amount of heat required to change the temperature of a substance.

Understanding Heat Capacity

concept

Heat Capacity

Video duration:

31s

Heat Capacity Video Summary

Heat capacity is a fundamental concept in thermodynamics that describes how a substance responds to the application of heat. When heat is added to an object, its temperature increases, demonstrating a direct relationship between the amount of heat applied and the resulting temperature change. This relationship can be expressed mathematically as:

q ∝ ΔT

In this equation, q represents the heat added to the substance, and ΔT is the change in temperature. The proportionality indicates that as the heat (q) increases, the temperature change (ΔT) also increases, assuming the substance's heat capacity remains constant. Understanding this relationship is crucial for predicting how different materials will respond to heat, which has practical applications in various scientific and engineering fields.

example

Heat Capacity Example 1

Video duration:

33s

Heat Capacity Example 1 Video Summary

When analyzing the relationship between heat and temperature change, it's essential to understand that heat (denoted as q) is directly proportional to the change in temperature. In this scenario, the temperature of a water bath increases from 25 Kelvin to 50 Kelvin. This represents a change of:

$ΔT = 50 - 25 = 25$

Since the temperature change is significant, we can observe that the temperature effectively doubles when considering the initial and final states. Because heat is directly proportional to temperature change, if the temperature doubles, the amount of heat must also double. Therefore, if the temperature increases from 25 Kelvin to 50 Kelvin, the heat transfer will also double, confirming that the correct conclusion is that the amount of heat increases accordingly.

concept

Heat Capacity

Video duration:

Heat Capacity Video Summary

Heat capacity, denoted by the capital letter C, refers to the amount of heat required to change the temperature of a substance. The relationship is straightforward: the more heat applied, the greater the temperature change observed. This concept can be further divided into specific heat capacity and molar heat capacity, each serving a distinct purpose in thermodynamics.

Specific heat capacity, represented by the lowercase c, quantifies the heat needed to raise the temperature of 1 gram of a substance by 1 degree Celsius (°C) or 1 Kelvin (K). This measurement is crucial for understanding how different materials respond to heat. In contrast, molar heat capacity, indicated by the capital C, measures the heat required to change the temperature of 1 mole of a substance by 1 degree, also in either °C or K. Molar heat capacity provides a more focused perspective, particularly useful in chemical reactions where moles are a standard unit of measurement.

The formula for molar heat capacity is expressed as:

$ C = \frac{q}{n \Delta T} $

In this equation, C represents molar heat capacity in joules per mole per degree Celsius (J/mol·°C) or joules per mole per Kelvin (J/mol·K), q is the heat added, n is the number of moles, and ΔT is the change in temperature. It is essential that the temperature units correspond to those used for molar heat capacity.

On the other hand, the specific heat capacity is defined by the formula:

$ c = \frac{q}{m \Delta T} $

Here, c is the specific heat capacity in joules per gram per degree Celsius (J/g·°C) or joules per gram per Kelvin (J/g·K), m is the mass of the substance in grams, and ΔT again represents the temperature change. As with molar heat capacity, it is crucial that the temperature units align with those specified for specific heat capacity.

Understanding the distinction between molar heat capacity and specific heat capacity is vital for accurately applying these concepts in various scientific contexts, particularly in chemistry and physics.

example

Heat Capacity Example 2

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Heat Capacity Example 2 Video Summary

To determine the molar heat capacity of silver, we start with the formula for molar heat capacity, represented as $ C $, which is defined as:

$ C = \frac{q}{n \Delta T} $

In this equation, $ q $ represents the heat absorbed, $ n $ is the number of moles, and $ \Delta T $ is the change in temperature. In this scenario, silver absorbs $ 6,845.5 $ joules of energy, indicating that $ q = +6,845.5 \, \text{J} $. The temperature increase is given as $ 17.2 \, \text{°C} $, which serves as our $ \Delta T $.

Next, we need to calculate the number of moles of silver. Given that the mass of silver is $ 15.7 \, \text{g} $ and the molar mass of silver is $ 107.87 \, \text{g/mol} $, we can find the number of moles $ n $ using the formula:

$ n = \frac{\text{mass}}{\text{molar mass}} = \frac{15.7 \, \text{g}}{107.87 \, \text{g/mol}} \approx 0.145548 \, \text{mol} $

Now, substituting the values into the molar heat capacity formula:

$ C = \frac{6,845.5 \, \text{J}}{0.145548 \, \text{mol} \times 17.2 \, \text{°C}} $

Calculating this gives:

$ C \approx 2734.45 \, \text{J/(mol} \cdot \text{°C)} $

Considering significant figures, we round this to $ 2.73 \times 10^3 \, \text{J/(mol} \cdot \text{°C)} $. Thus, the molar heat capacity of silver under the given conditions is approximately $ 2.73 \times 10^3 \, \text{J/(mol} \cdot \text{°C)} $.

concept

Heat Capacity

Video duration:

44s

Heat Capacity Video Summary

In thermodynamics, the concept of specific heat capacity is crucial for understanding how substances absorb or release heat. The relationship can be expressed through the formula $ q = mc\Delta T $, where $ q $ represents the amount of heat absorbed or released, $ m $ is the mass of the substance, $ c $ is the specific heat capacity, and $ \Delta T $ is the change in temperature. This equation is often remembered by the acronym MCAT, which stands for the Medical College Admission Test, a significant exam for pre-med students.

By rearranging this formula, students can easily calculate the heat transfer in various chemical reactions or physical processes. The specific heat capacity $ c $ indicates how much heat is required to change the temperature of a unit mass of a substance by one degree Celsius. Understanding this relationship is essential for predicting how substances will behave under different thermal conditions, making it a fundamental concept in both chemistry and physics.

example

Heat Capacity Example 3

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Heat Capacity Example 3 Video Summary

To calculate the heat released when 120 grams of water cools from 90 degrees Celsius to 45 degrees Celsius, we can use the formula for heat transfer:

q = mcΔT

In this equation, q represents the heat absorbed or released (in joules), m is the mass of the substance (in grams), c is the specific heat capacity (in joules per gram per degree Celsius), and ΔT is the change in temperature (in degrees Celsius).

Given that the specific heat capacity of water is c = 4.184 J/g°C, the mass of water is m = 120 g, and the change in temperature is calculated as:

ΔT = T_final - T_initial = 45°C - 90°C = -45°C

Now, substituting the values into the equation:

q = (120 g)(4.184 J/g°C)(-45°C)

Calculating this gives:

q = -22593.6 J

To convert joules to kilojoules, we use the conversion factor where 1 kJ = 1000 J. Thus:

q = -22593.6 J × (1 kJ / 1000 J) = -22.5936 kJ

Considering significant figures, we round the result to two significant figures based on the temperature measurement:

q ≈ -23 kJ

This indicates that approximately 23 kilojoules of heat are released as the water cools from 90 degrees Celsius to 45 degrees Celsius.

Problem

A sample of copper absorbs 3.53 kJ of heat, which increases the temperature by 25 ºC, determine the mass (in kg) of the copper sample if the specific heat capacity of copper is 0.385 J / g  ºC.

0.73 kg

0.35 kg

0.37 kg

0.53 kg

Problem

Based on their given specific heat capacities which compound would show the greatest temperature change upon absorbing 25.0 J of heat?

250.0 g Al

250.0 g Cu

250.0 g ethanol

250.0 g wood

Problem

50.00 g of heated metal ore is placed into an insulated beaker containing 822.5 g of water. Once the metal heats up the final temperature of the water is 32.08 ºC. If the metal gains 14.55 kJ of energy, what is the initial temperature of the water? The specific heat capacity of copper is 4.184 J / g  ºC.

23.86 °C

32.86 °C

63.08 °C

36.31 °C

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Here’s what students ask on this topic:

What is the difference between specific heat capacity and molar heat capacity?

Specific heat capacity (c) is the amount of heat required to raise the temperature of 1 gram of a substance by 1 degree Celsius or Kelvin. It is expressed in units of J/g·°C or J/g·K. The formula is $q = m c ΔT$ , where $q$ is heat, $m$ is mass, and $ΔT$ is the temperature change. Molar heat capacity (C) is the amount of heat required to raise the temperature of 1 mole of a substance by 1 degree Celsius or Kelvin. It is expressed in units of J/mol·°C or J/mol·K. The formula is $C = \frac{q}{n} ΔT$ , where $q$ is heat, $n$ is moles, and $ΔT$ is the temperature change.

How do you calculate the amount of heat absorbed or released using specific heat capacity?

To calculate the amount of heat absorbed or released using specific heat capacity, you can use the formula $q = m c ΔT$ . Here, $q$ represents the heat absorbed or released, $m$ is the mass of the substance in grams, $c$ is the specific heat capacity in J/g·°C or J/g·K, and $ΔT$ is the change in temperature in degrees Celsius or Kelvin. By multiplying these values, you can determine the total heat energy involved in the process.

Why is it important to match the units of temperature when using heat capacity formulas?

It is crucial to match the units of temperature when using heat capacity formulas to ensure consistency and accuracy in calculations. For specific heat capacity, the formula is $q = m c ΔT$ , and for molar heat capacity, it is $C = \frac{q}{n} ΔT$ . If the temperature change $ΔT$ is in degrees Celsius, the heat capacity should also be in units that correspond to degrees Celsius (e.g., J/g·°C or J/mol·°C). Similarly, if the temperature change is in Kelvin, the heat capacity should be in units that correspond to Kelvin (e.g., J/g·K or J/mol·K). This ensures that the calculated heat energy is accurate and meaningful.

What is the formula for molar heat capacity and how is it used?

The formula for molar heat capacity (C) is $C = \frac{q}{n} ΔT$ , where $q$ is the amount of heat absorbed or released, $n$ is the number of moles of the substance, and $ΔT$ is the change in temperature. This formula is used to determine the heat capacity per mole of a substance, which is useful in understanding how much heat is required to change the temperature of a given amount of substance. It is particularly important in chemical reactions and thermodynamic calculations.

How does the concept of heat capacity apply to chemical reactions?

Heat capacity is crucial in chemical reactions because it helps determine the amount of heat absorbed or released during the reaction. By knowing the specific or molar heat capacity of the reactants and products, you can calculate the heat change using the formulas $q = m c ΔT$ for specific heat capacity and $C = \frac{q}{n} ΔT$ for molar heat capacity. This information is essential for understanding reaction energetics, predicting temperature changes, and designing processes that require precise thermal management. It also aids in calculating enthalpy changes and understanding the thermodynamic properties of the substances involved.

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