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Multiple Choice
A car tire is inflated to a pressure of 2.00 atm at a temperature of 300 K. If the temperature increases to 360 K and the volume of the tire remains constant, what is the new pressure of the tire? (Assume the amount of gas does not change.)
A
2.40 atm
B
2.20 atm
C
3.00 atm
D
1.67 atm
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Verified step by step guidance
1
Identify the known variables: initial pressure \(P_1 = 2.00\) atm, initial temperature \(T_1 = 300\) K, final temperature \(T_2 = 360\) K, and volume remains constant.
Recognize that since the volume and amount of gas are constant, the pressure and temperature are related by Gay-Lussac's Law, which states \(\frac{P_1}{T_1} = \frac{P_2}{T_2}\).
Rearrange the equation to solve for the final pressure \(P_2\): \(P_2 = P_1 \times \frac{T_2}{T_1}\).
Substitute the known values into the equation: \(P_2 = 2.00 \times \frac{360}{300}\).
Calculate the value of \(P_2\) to find the new pressure of the tire after the temperature increase.