A car tire is initially inflated to a pressure of 2.0 atm at a temperature of 300 K. After driving, the temperature inside the tire increases to 360 K, while the volume and amount of gas remain constant. According to the ideal gas law, what is the new pressure of the tire?

• A. 3.6 atm
• B. 1.7 atm
• C. 2.0 atm
• D. 2.4 atm

Answer: (D)

Verified step by step guidance

1. Identify the known variables: initial pressure \(P_1 = 2.0\ \text{atm}\), initial temperature \(T_1 = 300\ \text{K}\), final temperature \(T_2 = 360\ \text{K}\), and note that volume and amount of gas remain constant.
2. Recall that for a fixed amount of gas at constant volume, 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: \(P_2 = 2.0\ \text{atm} \times \frac{360\ \text{K}}{300\ \text{K}}\).
5. Calculate the ratio and multiply to find the new pressure \(P_2\), which will give the pressure inside the tire after the temperature increase.