Question

A man buys a set of cheap tires for his Ford Pinto and puts them on his car in December. The temperature that day is -3.00°C. He inflates the tires to 2.18 ATM, knowing that if the tire pressure gets above 2.70 ATM they will burst. In the summer, he drives to Death Valley, where the temperature is 49.0°C. Will he need to stop and change a blown tire?

a) Yes, he will need to stop and change a blown tire.
b) No, he will not need to change a blown tire.
c) It's uncertain if he needs to stop and change a blown tire.
d) None of the above.

Answer 1

Using the ideal gas law, the tire pressure at 49.0°C is calculated to be approximately 2.62 ATM, which is below the burst threshold of 2.70 ATM. Therefore, the tires will not burst, and the man will not need to stop and change a blown tire.

Step-by-step explanation:

To determine if the tire pressure will exceed the burst threshold in Death Valley, we can use the ideal gas law which states that pressure is directly proportional to temperature, assuming the volume and number of moles of gas remain constant. This relationship is given by the formula: P1/T1 = P2/T2, where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature, respectively. Converting temperatures to Kelvin to use in the formula, we get -3.00°C + 273.15 = 270.15K for the initial temperature, and 49.0°C + 273.15 = 322.15K for the final temperature. Substituting the known values into the equation: 2.18 ATM / 270.15K = P2 / 322.15K, we can solve for P2. The calculation gives P2 ≈ 2.62 ATM, which is below the burst threshold of 2.70 ATM. Therefore, the answer is b) No, he will not need to change a blown tire.