Specific Heat & Temperature Changes: Videos & Practice Problems

Heat (q) is the transfer of energy between substances due to a temperature difference, while temperature (T) measures the kinetic energy of molecules. The equation q = mc⁢Δt relates heat to mass (m), specific heat capacity (c), and temperature change (Δt). Specific heat indicates how resistant a material is to temperature changes; higher values require more energy to change temperature. Understanding these concepts is crucial for grasping thermodynamics and energy transfer in physical systems.

Specific Heat & Temperature Changes

In the study of thermodynamics, understanding the concepts of heat and temperature is crucial. Temperature, denoted by the letter T, is a measure of the average kinetic energy of the molecules in a substance, indicating how hot or cold it is. For instance, a substance at 20 degrees Celsius has molecules moving faster than those at 10 degrees Celsius, resulting in a higher temperature.

Heat, represented by q, differs from temperature in that it refers to the transfer of energy between two materials due to a temperature difference. This transfer occurs from hotter to colder substances until thermal equilibrium is reached, where no further heat transfer occurs. At this point, the temperatures of the two substances equalize, and q becomes zero.

When a material absorbs or loses heat, it experiences a change in temperature. The relationship between heat transfer and temperature change is expressed by the equation:

\( q = mc \Delta T \)

In this equation, m represents the mass of the object, c is the specific heat capacity of the material, and \(\Delta T\) is the change in temperature. Specific heat is a measure of a material's resistance to temperature change, indicating how much heat is required to change the temperature of a unit mass of the substance by one degree Celsius. For example, water has a high specific heat capacity of approximately 4186 J/(kg·°C), meaning it requires more energy to change its temperature compared to metals like copper or iron, which have lower specific heats.

To illustrate this concept, consider the example of heating 50 grams of water from 40 to 55 degrees Celsius. The mass m is 0.05 kg, the specific heat c for water is 4186 J/(kg·°C), and the temperature change \(\Delta T\) is 15 degrees Celsius. Plugging these values into the equation gives:

\( q = 0.05 \, \text{kg} \times 4186 \, \text{J/(kg·°C)} \times 15 \, \text{°C} = 3140 \, \text{J} \)

This calculation shows that 3140 joules of heat are required to raise the temperature of the water by 15 degrees Celsius. Understanding these principles of heat transfer and specific heat is essential for grasping the broader concepts of thermodynamics and energy exchange in physical systems.

You are given a sample of an unknown metal. You weigh the sample and find that its weight is 29.4N. You add 1.25×10⁴ J of heat energy to the sample and find that its temperature increases from 52°C to 70°C. What is the specific heat of this unknown metal?

• A. 23.6 J/(kg⋅K)
• B. 231.5 J/(kg⋅K)
• C. 14.3 J/(kg⋅K)
• D. 1.20×10⁴ J/(kg⋅K)

Answer: (B)

Heating Cup of Water

In this scenario, we are examining the process of heating water using a hot plate rated at 200 watts. The goal is to determine the time required for the water to increase in temperature from 10 degrees Celsius to 90 degrees Celsius. To solve this, we will utilize the relationship between energy, power, and time.

First, we recognize that the energy transferred to the water, denoted as \( Q \), can be calculated using the specific heat formula:

\[ Q = m \cdot c \cdot \Delta T \]

Here, \( m \) represents the mass of the water, \( c \) is the specific heat capacity of water (approximately 4186 J/kg·°C), and \( \Delta T \) is the change in temperature. In this case, the change in temperature is:

\[ \Delta T = 90°C - 10°C = 80°C \]

Next, we need to find the time \( \Delta t \) it takes for this energy transfer to occur. The power equation relates power \( P \) to work done (or energy transferred) over time:

\[ P = \frac{W}{\Delta t} \]

Since work (or energy) can be represented as \( Q \), we can rearrange this equation to solve for time:

\[ \Delta t = \frac{Q}{P} \]

Substituting the expression for \( Q \) into this equation gives us:

\[ \Delta t = \frac{m \cdot c \cdot \Delta T}{P} \]

Now, we can plug in the values:

• Mass of water, \( m = 0.3 \) kg
• Specific heat of water, \( c = 4186 \) J/kg·°C
• Change in temperature, \( \Delta T = 80 \) °C
• Power of the hot plate, \( P = 200 \) W

Calculating \( Q \):

\[ Q = 0.3 \, \text{kg} \cdot 4186 \, \text{J/kg·°C} \cdot 80 \, \text{°C} = 100,464 \, \text{J} \]

Now substituting \( Q \) into the time equation:

\[ \Delta t = \frac{100,464 \, \text{J}}{200 \, \text{W}} = 502.32 \, \text{s} \]

This results in approximately 500 seconds, which is equivalent to about 8.3 minutes. Therefore, it will take roughly 8 and a half minutes to heat the water from 10 degrees Celsius to 90 degrees Celsius.

Here’s what students ask on this topic:

What is the difference between heat and temperature in physics?

In physics, heat (q) is the transfer of energy between substances due to a temperature difference, while temperature (T) measures the kinetic energy of molecules within a substance. Temperature is a measure of how hot or cold an object is, given in degrees Celsius, Kelvin, etc. Heat, on the other hand, is energy in transit and is measured in joules (J). Heat flows from a hotter object to a colder one until thermal equilibrium is reached. Understanding this distinction is crucial for studying thermodynamics and energy transfer.

How do you calculate the amount of heat required to change the temperature of a substance?

The amount of heat (q) required to change the temperature of a substance can be calculated using the equation:

$q=mc∆T$

where $m$ is the mass of the substance, $c$ is the specific heat capacity, and $∆T$ is the change in temperature. The specific heat capacity is a material-specific constant that indicates how much energy is needed to change the temperature of 1 kg of the substance by 1 degree Celsius.

What is specific heat capacity and why is it important?

Specific heat capacity (c) is a property of a material that indicates how much heat energy is required to raise the temperature of 1 kg of the material by 1 degree Celsius. It is important because it helps us understand how different materials respond to heat. Materials with high specific heat capacities require more energy to change their temperature, making them more resistant to temperature changes. This concept is crucial in fields like thermodynamics, engineering, and environmental science.

Why does water have a high specific heat capacity compared to metals?

Water has a high specific heat capacity (4186 J/kg·°C) compared to metals like iron or copper because of its molecular structure and hydrogen bonding. These bonds require more energy to break, meaning more heat is needed to increase the temperature of water. This property makes water an excellent coolant and helps regulate temperatures in natural and engineered systems.

How does the specific heat capacity affect the rate of temperature change in a substance?

The specific heat capacity (c) of a substance affects the rate of temperature change by determining how much heat energy is required to change its temperature. A substance with a high specific heat capacity will change temperature more slowly when the same amount of heat is applied, compared to a substance with a low specific heat capacity. This is because more energy is needed to increase the temperature of materials with higher specific heat capacities.