What are the units of specific heat capacity?

Question

Accepted Answer

The correct option is (3):

Specific heat capacity, often denoted as $c$, is a fundamental property of a substance that quantifies the amount of heat energy required to raise the temperature of a unit mass of that substance by one degree (Celsius or Kelvin). The formula that relates heat energy ($Q$), mass ($m$), specific heat capacity ($c$), and change in temperature ($\Delta T$) is given by:
$Q = mc\Delta T$

To find the units of specific heat capacity ($c$), we can rearrange this formula:
$c = \frac{Q}{m\Delta T}$

Now, let's substitute the SI units for each quantity:  * $Q$ (Heat energy) is measured in Joules (J).
  * $m$ (Mass) is measured in kilograms (kg).
  * $\Delta T$ (Change in temperature) is measured in Kelvin (K).Therefore, the SI unit for specific heat capacity ($c$) becomes:
$c = \frac{	ext{J}}{	ext{kg} \cdot 	ext{K}}$

This can be written using negative exponents as $J \cdot kg^{-1} \cdot K^{-1}$. This unit clearly indicates that specific heat capacity represents the energy per unit mass per unit temperature change.

The incorrect option is (1): J kg K
This option suggests that heat capacity increases with mass and temperature change in a direct product relationship, which is dimensionally incorrect. The unit J kg K would imply that heat is directly proportional to mass and temperature in a way that doesn't align with the definition of specific heat capacity as energy per unit mass per unit temperature.

The incorrect option is (2): $J\~kg^{-1}K$
This option incorrectly places Kelvin (K) in the numerator. Specific heat capacity is inversely proportional to the change in temperature, meaning temperature should be in the denominator, or have a negative exponent when written linearly.

The incorrect option is (4): $J^{-1}kg\~K^{-1}$
This option incorrectly places Joules (J) in the denominator (or with a negative exponent of -1), suggesting an inverse relationship with energy. Specific heat capacity is directly proportional to the energy absorbed or released, so Joules should be in the numerator.