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

Answer: (A)

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.
2. Recognize that since the volume and amount of gas are constant, the pressure and temperature are related by Gay-Lussac's Law, which states \(\frac{P_1}{T_1} = \frac{P_2}{T_2}\).
3. Rearrange the equation to solve for the final pressure \(P_2\): \(P_2 = P_1 \times \frac{T_2}{T_1}\).
4. Substitute the known values into the equation: \(P_2 = 2.00 \times \frac{360}{300}\).
5. Calculate the value of \(P_2\) to find the new pressure of the tire after the temperature increase.