Answer:
Therefore,
The pressure of the gas will be 1/5th of the original.
[tex]P_{2}=\dfrac{1}{5}P_{1}[/tex]
Explanation:
Given:
Let V₁ , P₁, and T₁ be the original Volume , Pressure and Temperature,
Now it Changes to V₂ , P₂ , and T₂
[tex]V_{2}=5\times V_{1}\\T_{2}=T_{1}=constant[/tex]
To Find:
What happens to the new pressure
[tex]P_{2}=?[/tex]
Solution:
Combined Gas Law:
The combined gas law combines the three gas laws:
Boyle's Law, Charles' Law, and Gay-Lussac's Law.
It states that the ratio of the product of pressure and volume and the absolute temperature of a gas is equal to a constant.
Hence,
[tex]\dfrac{P_{1}V_{1}}{T_{1}}=\dfrac{P_{2}V_{2}}{T_{2}}[/tex]
Substituting the values [tex]V_{2}=5\times V_{1}\\T_{2}=T_{1}=constant[/tex] we get, T₁ and T₂ , V₁ will get cancelled,
[tex]P_{2}=\dfrac{1}{5}P_{1}[/tex]
That is Pressure decreases by [tex]\dfrac{1}{5}[/tex]
Therefore,
The pressure of the gas will be 1/5th of the original.
[tex]P_{2}=\dfrac{1}{5}P_{1}[/tex]