Question

which units express specific heat capacity?

option 1:
\\(\text{j}/^{\circ}\text{c}\\), \\(\text{j}/\text{k}\\), \\(\text{cal}/^{\circ}\text{c}\\), \\(\text{cal}/\text{k}\\)

option 2:
\\(^{\circ}\text{c}\\), \\(\text{k}\\)

option 3:
\\(\text{j}\\), \\(\text{cal}\\)

option 4:
\\(\text{j}/(\text{g}\cdot^{\circ}\text{c})\\), \\(\text{j}/(\text{g}\cdot\text{k})\\), \\(\text{cal}/(\text{g}\cdot^{\circ}\text{c})\\), \\(\text{cal}/(\text{g}\cdot\text{k})\\)

Explanation:

Define specific heat capacity

$$ c = \frac{q}{m \cdot \Delta T} $$

Identify units for each variable

$$
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$$

Determine combined units

$$ \frac{\text{J}}{\text{g} \cdot \text{°C}}, \quad \frac{\text{J}}{\text{g} \cdot \text{K}}, \quad \frac{\text{cal}}{\text{g} \cdot \text{°C}}, \quad \frac{\text{cal}}{\text{g} \cdot \text{K}} $$

Answer:

• (A) \(\text{J/°C, J/K, cal/°C, cal/K}\)
• (B) \(\text{°C, K}\)
• (C) \(\text{J, cal}\)
• (D) \(\text{J/(g}\cdot\text{°C), J/(g}\cdot\text{K), cal/(g}\cdot\text{°C), cal/(g}\cdot\text{K)}\) (Correct answer)