10.2.3 - Example of Heat Calculation
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Introduction to Specific Heat Capacity
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Today, we’re going to talk about specific heat capacity. Can anyone explain what specific heat capacity is?
Isn’t it how much heat is needed to raise the temperature of a certain mass of a substance by one degree?
Exactly! Great job, Student_1. It’s measured in J/kg°C. Now, when we want to calculate heat energy, we use the formula Q = mcΔT. Can someone tell me what each symbol represents?
Q is the heat energy, m is the mass, c is specific heat capacity, and ΔT is the temperature change!
Perfect! If we know all these values, we can figure out how much heat energy is needed. Now, let’s dive into a practical example.
Example Calculation of Heat Energy
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Let's calculate the heat needed to heat 2 kg of water from 20°C to 100°C. Who remembers the specific heat capacity of water?
It's 4.18 kJ/kg°C, or 4180 J/kg°C.
Correct! Now, if we plug our values into the formula Q = mcΔT, we have m as 2 kg, c as 4180 J/kg°C, and ΔT as the final temperature minus the initial temperature, or 100°C - 20°C.
So that’s a ΔT of 80°C!
Yes! Now, can someone calculate Q?
Q = 2 × 4180 × 80, which equals 669600 J.
Excellent work! So, to heat 2 kg of water from 20°C to 100°C, we need 669600 Joules, or 669.6 kJ.
Practical Applications
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Now that we've calculated our example, let’s consider where we might use this in daily life. Can anyone think of examples?
Cooking! When I boil water, I remember it takes time to get the water hot.
What about in heating systems? They need to know how much energy is needed to raise the temperature of water, right?
Absolutely! Understanding specific heat capacity helps us in various scenarios, from cooking to industrial processes. Remember, the more you know about heat calculations, the better decisions you can make regarding energy use.
Introduction & Overview
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Quick Overview
Standard
In this section, we explore an example of calculating the heat required to raise the temperature of water using its specific heat capacity. The calculation showcases how mass, specific heat capacity, and temperature change play crucial roles in determining the total heat energy needed.
Detailed
In this section, we examine the process of calculating heat energy using the formula Q = mcΔT. Here, Q represents the heat energy (in Joules), m is the mass of the substance (in kilograms), c is the specific heat capacity (in J/kg°C), and ΔT is the change in temperature (in °C). A practical example is provided, where we aim to determine how much heat is needed to heat 2 kg of water from 20°C to 100°C with a specific heat capacity of 4.18 kJ/kg°C. Through the calculation, we find that the required heat is 669.6 Joules. This example illustrates the application of the specific heat capacity formula in real-world scenarios, highlighting its significance in understanding thermal energy transfer.
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Heat Calculation for Water
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Chapter Content
To heat 2 kg of water from 20°C to 100°C, with a specific heat capacity of 4.18 kJ/kg°C, the heat required is:
Q=2×4.18×(100−20)=2×4.18×80=669.6 J
Q = 2 \times 4.18 \times (100 - 20) = 2 \times 4.18 \times 80 = 669.6 \, \text{J}
Hence, 669.6 Joules of heat is required to heat the water.
Detailed Explanation
This calculation demonstrates how to find the amount of heat needed to raise the temperature of water. Here, we're trying to heat 2 kilograms of water from an initial temperature of 20°C to a final temperature of 100°C.
- Specific Heat Capacity: The specific heat capacity of water is given as 4.18 kJ/kg°C. This value represents the amount of heat needed to raise the temperature of one kilogram of water by one degree Celsius.
- Formula: We use the formula Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
- Calculate ΔT: First, calculate the temperature change (ΔT): 100°C - 20°C = 80°C.
- Plugging Values: Now plug the values into the formula: Q = 2 kg * 4.18 kJ/kg°C * 80°C.
- Final Calculation: This means Q = 2 × 4.18 × 80 = 669.6 J. This is the total amount of heat required to heat the water.
So, the result shows that 669.6 Joules of heat energy needs to be added to the water to achieve this temperature increase.
Examples & Analogies
Imagine heating a large pot of water to make pasta. You start with cold water at room temperature and then turn the stove on. The heat from the stove transfers to the water, raising its temperature. The pot has to add enough heat energy to not only change the water's temperature but also to keep it at a rolling boil to cook properly. Similarly, this calculation helps understand the precise amount of energy required to make such a temperature change.
Key Concepts
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Specific Heat Capacity: The heat required to raise the temperature of a unit mass by 1°C.
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Heat Calculation: Using the formula Q = mcΔT to find out how much heat energy is needed.
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Units of Measurement: Heat is measured in Joules, mass in kilograms, and specific heat capacity in J/kg°C.
Examples & Applications
Calculating the heat to raise 3 kg of olive oil from 25°C to 125°C with a specific heat capacity of 2.0 kJ/kg°C.
Determining heat energy needed to heat 5 kg of aluminum from room temperature (20°C) to 100°C with a specific heat capacity of 0.9 kJ/kg°C.
Memory Aids
Interactive tools to help you remember key concepts
Rhymes
Heat it up, heat it high, two kg of water, don't be shy. Q is what you need to see, mcΔT, that’s the key.
Stories
Once upon a time, a pot of water wanted to boil. To raise its temperature, it needed energy, calculated easily with Q = mcΔT. And so, the pot filled with warmth.
Memory Tools
Remember 'Heat = Mass × C × ΔT' with the mnemonic 'Happy Mice Celebrate Daily Time'.
Acronyms
Use 'QMC' to remember
for heat
for mass
for specific heat
and pretend C means change too.
Flash Cards
Glossary
- Heat Energy (Q)
The energy transferred due to temperature differences, measured in Joules.
- Mass (m)
The amount of substance, typically measured in kilograms.
- Specific Heat Capacity (c)
The amount of heat per unit mass required to raise the temperature by one degree Celsius, measured in J/kg°C.
- Temperature Change (ΔT)
The difference between the initial and final temperature, measured in degrees Celsius.
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