You can calculate mass from a temperature change if you know the amount of heat transferred, the specific heat capacity of the substance, and the change in temperature.
Here's how it works, explained in detail:
The Formula: Specific Heat Capacity
The relationship between heat, mass, specific heat capacity, and temperature change is defined by the following formula:
Q = m c ΔT
Where:
- Q = Heat transferred (in Joules or Calories)
- m = Mass of the substance (in grams or kilograms) - This is what we want to find.
- c = Specific heat capacity of the substance (in J/g°C or cal/g°C) - This value is unique to each substance and represents the amount of heat required to raise the temperature of 1 gram of the substance by 1 degree Celsius.
- ΔT = Change in temperature (in °C or Kelvin) - This is calculated as the final temperature minus the initial temperature (ΔT = Tfinal - Tinitial).
Rearranging the Formula to Solve for Mass
To calculate the mass (m), we need to rearrange the formula:
*m = Q / (c ΔT)**
Steps to Calculate Mass
- Determine the heat transferred (Q): This value will usually be provided in the problem. It represents the amount of energy added to or removed from the substance.
- Identify the specific heat capacity (c): This value depends on the substance. You can find specific heat capacities in reference tables or online. Some common examples:
- Water (liquid): 4.186 J/g°C or 1.00 cal/g°C
- Aluminum: 0.900 J/g°C
- Copper: 0.385 J/g°C
- Calculate the change in temperature (ΔT): Subtract the initial temperature from the final temperature. Ensure the temperature is in Celsius or Kelvin. The change in temperature is the same whether you use Celsius or Kelvin (since the size of the degree is the same).
- Plug the values into the formula: Substitute the values of Q, c, and ΔT into the rearranged formula: m = Q / (c * ΔT).
- Calculate the mass (m): Perform the calculation to find the mass. Make sure your units are consistent. For example, if Q is in Joules and c is in J/g°C, then the mass will be in grams.
Example
Let's say you heat a piece of copper and transfer 500 Joules of heat to it. The temperature of the copper increases from 20°C to 45°C. What is the mass of the copper?
- Q = 500 J
- c = 0.385 J/g°C (specific heat capacity of copper)
- ΔT = 45°C - 20°C = 25°C
Now, plug these values into the formula:
m = 500 J / (0.385 J/g°C * 25°C)
m = 500 J / 9.625 J/g
m ≈ 51.95 g
Therefore, the mass of the copper is approximately 51.95 grams.
Important Considerations
- Units: Ensure all units are consistent before performing the calculation. Convert units if necessary.
- Phase Changes: This formula only applies when there is no phase change (e.g., melting, boiling). During a phase change, the temperature remains constant while heat is added or removed. Different formulas are used to calculate heat transfer during phase changes.
- Accuracy: The accuracy of the calculated mass depends on the accuracy of the values for Q, c, and ΔT.
