When the absolute pressure of a confined gas doubles while the volume remains constant, the temperature of the gas also increases. To understand why, we can use the Ideal Gas Law, which is stated as:
\[ PV = nRT \]
Here:
- \( P \) is the pressure,
- \( V \) is the volume,
- \( n \) is the number of moles of gas,
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin.
Given that the volume \( V \) and the number of moles \( n \) of the gas remain constant, we can analyze how changes in pressure \( P \) affect the temperature \( T \).
Starting with the Ideal Gas Law, we rearrange it to solve for temperature:
\[ T = \frac{PV}{nR} \]
Since \( V \), \( n \), and \( R \) are constants in this scenario, we can write:
\[ T \propto P \]
This equation shows that temperature \( T \) is directly proportional to pressure \( P \) when volume \( V \) is constant. Therefore, if the pressure \( P \) doubles, the temperature \( T \) must also double to maintain the equality.
So, if the absolute pressure of the confined gas doubles while the volume remains the same, the temperature of the gas will also double.
