Considering the Gay- Lussac's Law, the pressure on a cold winter day is 26.80 psi.
Gay-Lussac's law is one of the gas laws, which establishes the relationship between the temperature and the pressure of a gas when the volume is constant.
This law states that the pressure of the gas is directly proportional to its temperature. In other words, if the temperature increases, the pressure will increase, while if the temperature decreases, the pressure will decrease.
Gay-Lussac's law can be expressed mathematically as follows:
[tex]\frac{P}{T}=k[/tex]
Where P = pressure, T = temperature, k = Constant
This law indicates that the quotient between pressure and temperature is constant.
Studying two different states, an initial state 1 and a final state 2, it is satisfied:
[tex]\frac{P1}{T1}=\frac{P2}{T2}[/tex]
In this case, you know:
Replacing:
[tex]\frac{32 psi}{308 K}=\frac{P2}{258 K}[/tex]
Solving:
[tex]\frac{32 psi}{308 K}x258 K=P2[/tex]
P2= 26.80 psi
Finally, the pressure on a cold winter day is 26.80 psi.
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