Which of the following units correctly express specific heat capacity?

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

Answer: (B)

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: \(q = m \cdot c \cdot \Delta T\), where \(q\) is heat energy (in joules), \(m\) is mass (in kilograms or grams), \(c\) is specific heat capacity, and \(\Delta T\) is the temperature change (in Kelvin or Celsius).
3. From the formula, rearranging for specific heat capacity gives \(c = \frac{q}{m \cdot \Delta T}\), so the units of \(c\) must be energy per mass per temperature, i.e., joules per gram (or kilogram) per Kelvin.
4. Analyze the given options: units like \(J\,kg^{-1}\) lack the temperature term, \(J\,K^{-1}\) lack the mass term, and \(J\,mol^{-1}\,K^{-1}\) correspond to molar heat capacity, not specific heat capacity.
5. Therefore, the correct units for specific heat capacity must include energy, mass, and temperature terms, such as \(J\,g^{-1}\,K^{-1}\).