A

Step 1: Understand the definitions of specific heat capacities.
The specific heat at constant pressure, denoted as $C_p$, is defined as the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius while maintaining constant pressure.
Step 2: The specific heat at constant volume, denoted as $C_v$, is defined similarly, but the volume is kept constant during the heating process.
Step 3: Analyze why $C_p$ is always greater than $C_v$. When a gas is heated at constant pressure, it not only absorbs heat to increase its temperature but also does work to expand against the external pressure. Thus, the quantity of heat added at constant pressure must be greater than that added at constant volume where no work is done against external pressure.
Step 4: The relationship between them can be expressed as follows: $$C_p = C_v + R$$ where $R$ is the gas constant. This shows that $C_p$ is always greater than $C_v$ for any gas.
Conclusion: Therefore, the specific heat of a gas at constant pressure is always greater than its specific heat at constant volume.
Therefore, the correct answer is A.