How is temperature change for a pathway step used to determine the value for the amount of heat transferred?

General
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how is temperature change for a pathway step used to determine the value for the amount of heat transferred?

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How is temperature change for a pathway step used to determine the value for the amount of heat transferred?

Answer: To determine the amount of heat transferred during a temperature change, we use the concept of specific heat capacity. This involves a simple equation that relates heat transfer to temperature change, mass, and the specific heat capacity of the substance.

The Equation

The equation used is:

q = mc\Delta T

Where:

  • q is the heat transferred.
  • m is the mass of the substance.
  • c is the specific heat capacity, which is the amount of heat needed to raise the temperature of 1 gram of the substance by 1 degree Celsius.
  • \Delta T is the change in temperature, calculated as the final temperature minus the initial temperature.

Step-by-Step Explanation

  1. Measure the Mass (m): Determine the mass of the substance you are studying. It should be in grams.

  2. Determine the Temperature Change (\Delta T): Subtract the initial temperature from the final temperature to find \Delta T.

  3. Use the Specific Heat Capacity (c): Find the specific heat capacity of the substance. This value is unique to each material and is usually provided in joules per gram per degree Celsius (J/g°C).

  4. Calculate the Heat Transfer (q): Plug the values into the formula q = mc\Delta T to find the heat transferred. The result will give you the amount of heat in joules.

Example

Let’s say we have 100 grams of water (with a specific heat capacity of 4.18 J/g°C), and its temperature changes from 20°C to 30°C.

  1. Mass m: 100 grams
  2. Temperature change \Delta T: 30°C - 20°C = 10°C
  3. Specific heat capacity c: 4.18 J/g°C

Substitute these values into the formula:

q = (100 \, \text{g})(4.18 \, \text{J/g°C})(10 \, \text{°C})
q = 4180 \, \text{J}

So, 4180 joules of heat is transferred.

Summary: To find the amount of heat transferred due to a temperature change, use the formula q = mc\Delta T. Measure the mass, determine the temperature change, and use the specific heat capacity for the calculation. This method gives you the amount of heat transferred in a given pathway step.