Given:
[tex]P_{2} = \text{1.5 atm}[/tex]
[tex]T_{2} = \text{250 K}[/tex]
[tex]P_{1} = \text{1 atm}[/tex]
Required:
[tex]T_{1}[/tex]
Strategy:
This is a gas law problem. What gas law should we use?
Since the given quantities are pressure and temperature, we will use Gay-Lussac's law. According to this gas law, the pressure of a gas is directly proportional to its absolute temperature keeping the volume and the amount of gas constant.
Caution: The temperature must be converted to kelvin. If the given temperature is in degree Celsius, add 273 or 273.15 to convert it to kelvin.
The formula used for Gay-Lussac's law is
[tex]\boxed{\dfrac{P_{1}}{T_{1}} = \dfrac{P_{2}}{T_{2}}}[/tex]
where:
[tex]P_{1} = \text{initial pressure}[/tex]
[tex]T_{1} = \text{initial temperature}[/tex]
[tex]P_{2} = \text{final pressure}[/tex]
[tex]T_{2} = \text{final temperature}[/tex]
Solution:
Starting with the formula of Gay-Lussac's law
[tex]\dfrac{P_{1}}{T_{1}} = \dfrac{P_{2}}{T_{2}}[/tex]
Multiplying both sides of the equation by T₁T₂ to eliminate the denominators
[tex]P_{1}T_{2} = P_{2}T_{1}[/tex]
Dividing both sides of the equation by P₂ to solve for T₁
[tex]T_{1} = T_{2} \times \dfrac{P_{1}}{P_{2}}[/tex]
Substituting the given values and solving for T₁
[tex]T_{1} = \text{250 K} \times \dfrac{\text{1 atm}}{\text{1.5 atm}}[/tex]
Therefore, the initial temperature is
[tex]\boxed{T_{1} = \text{167 K}}[/tex]
Answer:
T₁ = 167 K
[tex]\\[/tex]
#BrainlyChallenge2021
