Notes on Specific Heat and Related Calculations

Specific Heat

• The specific heat of a substance is defined as the amount of heat required to raise the temperature of one gram of the substance by one degree Celsius.

Key Equation

• The relationship between the heat gained or released by a substance and its change in temperature is expressed by the equation:

  • q = ms riangle T
  • Where:
    • q = heat gained or released (in Joules)
    • m = mass of the substance (in grams)
    • s = specific heat of the substance (in J/g.°C)
    • riangle T = change in temperature (in °C)

• An alternate symbol for specific heat capacity is c, but in this context, the symbol s is used.

Rearranging the Equation

• To solve for m (mass of the substance), rearrange the equation:
  • m = \frac{q}{s\triangle T}

Example Calculation

• When a substance has a specific heat of 0.366 J/g.°C and is heated from 27.6 °C to 75.0 °C, it absorbs 426 J of heat. Calculate the mass of the substance:
  • Given:
  • Specific heat, s = 0.366 J/g.°C
  • Initial temperature = 27.6 °C
  • Final temperature = 75.0 °C
  • Change in temperature, riangle T = 75.0 °C - 27.6 °C = 47.4 °C
  • Heat absorbed, q = 426 J
  • Substitute the values into the rearranged equation:
  • m = \frac{426 ext{ J}}{0.366 ext{ J/g.°C} imes 47.4 ext{ °C}}
  • Calculate:
    • m = \frac{426}{17.2794} ≈ 24.6 ext{ g}

Additional Notes

• Be familiar with units of measurement and ensure that they are consistent throughout calculations.
• Understanding the concept of specific heat is essential in thermodynamics as it relates to heat transfer and material properties.