Which of the following is the correct SI unit for specific heat capacity?

• A. J kg^{-1} K^{-1}
• B. J mol^{-1} K^{-1}
• C. J K^{-1}
• D. kg J^{-1} K^{-1}

Answer: (A)

Verified step by step guidance

1. Understand that specific heat capacity is defined as the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Kelvin (or Celsius).
2. Recall the formula for specific heat capacity: \(q = m c \Delta T\), where \(q\) is heat energy in joules (J), \(m\) is mass in kilograms (kg), \(c\) is specific heat capacity, and \(\Delta T\) is the temperature change in kelvin (K).
3. Rearrange the formula to solve for specific heat capacity: \(c = \frac{q}{m \Delta T}\).
4. Analyze the units on the right side: heat energy \(q\) has units of joules (J), mass \(m\) has units of kilograms (kg), and temperature change \(\Delta T\) has units of kelvin (K). So, the units of \(c\) are \(\frac{J}{kg \cdot K}\).
5. Compare this derived unit with the options given and identify that the correct SI unit for specific heat capacity is \(J\ kg^{-1}\ K^{-1}\).