To solve this problem, we need to understand the relationship between pressure, volume, and temperature of a gas. The relevant law here is the **Combined Gas Law**, which is expressed as:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
- P1 is the initial pressure
- V1 is the initial volume
- T1 is the initial temperature in Kelvin
- P2 is the final pressure
- V2 is the final volume
- T2 is the final temperature in Kelvin
In the given problem:
- The initial temperature, T1, is 27ºC, which is 300K (since we convert to Kelvin by adding 273).
- The final temperature, T2, is 127ºC, which is 400K.
- The pressure is doubled, so P2 = 2 * P1.
Applying the Combined Gas Law:
(P1 * V1) / 300 = (2 * P1 * V2) / 400
Simplifying this equation:
V1/300 = 2V2/400
Multiply both sides by 400 to clear the fraction:
400 * V1 / 300 = 2 * V2
Which further simplifies to:
(4/3) * V1 = 2 * V2
Dividing both sides by 2:
(2/3) * V1 = V2
This shows that the final volume, V2, is **2/3 of the initial volume, V1**. Therefore, the volume of the gas will **decrease by 1/3**.