Heat Capacity Formula: Explained With Examples

by Olex Johnson 47 views

Hello! I'm here to help you understand the heat capacity formula. I'll explain it in detail, provide solved examples, and make sure you have a clear grasp of this important concept. Let's dive in!

Correct Answer

The heat capacity formula is: Q = mcΔT, where Q represents the heat energy transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

Detailed Explanation

Let's break down the heat capacity formula and understand each part thoroughly. Heat capacity is a crucial concept in thermodynamics, and knowing how to use the formula is essential for solving various problems.

What is Heat Capacity?

Heat capacity is the amount of heat energy required to raise the temperature of a substance by a certain amount. It tells us how much energy a substance can store as heat. There are two main types of heat capacity:

  1. Specific Heat Capacity (c): This is the amount of heat required to raise the temperature of 1 gram (or 1 kg) of a substance by 1 degree Celsius (or Kelvin). It is a property of the substance itself. Different substances have different specific heat capacities. For example, water has a high specific heat capacity, meaning it takes a lot of energy to heat it up.
  2. Molar Heat Capacity: This is the amount of heat required to raise the temperature of 1 mole of a substance by 1 degree Celsius (or Kelvin).

The Heat Capacity Formula: Q = mcΔT

The formula Q = mcΔT is used to calculate the heat energy (Q) transferred when the temperature of a substance changes. Let's define each term:

  • Q: This is the heat energy transferred, usually measured in Joules (J) or calories (cal). It's the amount of energy added to or removed from the substance.
  • m: This is the mass of the substance, measured in grams (g) or kilograms (kg).
  • c: This is the specific heat capacity of the substance, measured in J/g°C or J/kg°C. Each substance has a unique value for its specific heat capacity.
  • ΔT: This is the change in temperature, calculated as the final temperature (Tf) minus the initial temperature (Ti): ΔT = Tf - Ti. It is measured in degrees Celsius (°C) or Kelvin (K).

Units

It's important to pay attention to the units when using the heat capacity formula. Here's a summary:

  • Q (Heat Energy): Joules (J) or calories (cal)
  • m (Mass): grams (g) or kilograms (kg)
  • c (Specific Heat Capacity): J/g°C or J/kg°C
  • ΔT (Change in Temperature): °C or K

Make sure your units are consistent throughout the calculation to get the correct answer.

Solved Examples

Let's work through some examples to illustrate how to use the heat capacity formula:

Example 1:

How much heat is required to raise the temperature of 500 g of water from 20°C to 80°C? (The specific heat capacity of water is 4.184 J/g°C.)

Solution:

  1. Identify the knowns:
    • m = 500 g
    • c = 4.184 J/g°C
    • Ti = 20°C
    • Tf = 80°C
  2. Calculate ΔT:
    • ΔT = Tf - Ti = 80°C - 20°C = 60°C
  3. Use the formula Q = mcΔT:
    • Q = (500 g) * (4.184 J/g°C) * (60°C)
    • Q = 125,520 J

Answer: 125,520 Joules of heat is required.

Example 2:

A 2 kg block of aluminum (specific heat capacity = 0.9 J/g°C) is heated, and its temperature increases by 10°C. How much heat was added?

Solution:

  1. Identify the knowns:
    • m = 2 kg = 2000 g (convert kg to g)
    • c = 0.9 J/g°C
    • ΔT = 10°C
  2. Use the formula Q = mcΔT:
    • Q = (2000 g) * (0.9 J/g°C) * (10°C)
    • Q = 18,000 J

Answer: 18,000 Joules of heat was added.

Example 3:

If 1000 J of heat is added to 100 g of a substance, and its temperature increases from 25°C to 35°C, what is the specific heat capacity of the substance?

Solution:

  1. Identify the knowns:
    • Q = 1000 J
    • m = 100 g
    • Ti = 25°C
    • Tf = 35°C
  2. Calculate ΔT:
    • ΔT = Tf - Ti = 35°C - 25°C = 10°C
  3. Rearrange the formula to solve for c:
    • Q = mcΔT
    • c = Q / (m * ΔT)
  4. Plug in the values:
    • c = 1000 J / (100 g * 10°C)
    • c = 1 J/g°C

Answer: The specific heat capacity of the substance is 1 J/g°C.

Real-World Applications

The heat capacity formula has many practical applications. For instance:

  • Cooking: Understanding heat capacity helps in cooking, as different materials (pots, pans, food) heat up at different rates.
  • Engineering: Engineers use heat capacity calculations in designing engines, heat exchangers, and other thermal systems.
  • Climate Science: The heat capacity of the oceans plays a vital role in regulating the Earth's climate.

Key Takeaways

Here are the main points to remember:

  • The heat capacity formula is Q = mcΔT.
  • Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
  • Specific heat capacity (c) is a property of the substance.
  • Make sure to use consistent units.
  • The formula is used to calculate heat transfer in various applications, from cooking to engineering.

I hope this explanation helps you understand the heat capacity formula better. If you have more questions, feel free to ask!