A tire has a pressure of 780 mm Hg at 27^circ C If the tire is heated to 47^circ C on hot pavement, the new pressure will be: 830 mm Hg ) 280 mm Hg 590 mm Hg 310 mm Hg none of the above

To solve this problem, we can use the ideal gas law in the form of Gay-Lussac's Law, which relates pressure and temperature for a fixed amount of gas at constant volume. The formula is:<br /><br />\[<br />\frac{P_1}{T_1} = \frac{P_2}{T_2}<br />\]<br /><br />where:<br />- \( P_1 \) is the initial pressure,<br />- \( T_1 \) is the initial temperature in Kelvin,<br />- \( P_2 \) is the final pressure,<br />- \( T_2 \) is the final temperature in Kelvin.<br /><br />First, convert the temperatures from Celsius to Kelvin by adding 273.15:<br /><br />\[<br />T_1 = 27 + 273.15 = 300.15 \, \text{K}<br />\]<br />\[<br />T_2 = 47 + 273.15 = 320.15 \, \text{K}<br />\]<br /><br />Now, substitute the known values into the equation:<br /><br />\[<br />\frac{780 \, \text{mm Hg}}{300.15 \, \text{K}} = \frac{P_2}{320.15 \, \text{K}}<br />\]<br /><br />Solve for \( P_2 \):<br /><br />\[<br />P_2 = \frac{780 \times 320.15}{300.15}<br />\]<br /><br />Calculate \( P_2 \):<br /><br />\[<br />P_2 \approx \frac{249717}{300.15} \approx 831.8 \, \text{mm Hg}<br />\]<br /><br />The new pressure is approximately 831.8 mm Hg. Since this value does not exactly match any of the given options, the correct answer is "none of the above."