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

• A. J kg^{-1} K^{-1}
• B. J mol^{-1} K^{-1}
• C. J K^{-1}
• D. kg m^2 s^{-2} K^{-1}

Answer: (A)

Verified step by step guidance

1. Understand that specific heat capacity is defined as the amount of heat 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 specific heat capacity are \(\frac{J}{kg \cdot K}\).
5. Compare this derived unit with the options given to identify the correct SI unit for specific heat capacity.