Final answer:
To calculate the gauge pressure of car tires when the temperature drops, we use the Ideal Gas Law, relating initial and final pressure and temperature, assuming constant volume and amount of gas.
Step-by-step explanation:
The question involves calculating the change in gauge pressure of a car tire due to a change in temperature. This is a direct application of the Ideal Gas Law, which relates the pressure, volume, and temperature of an ideal gas. Assuming that the volume of the car tire and the amount of gas remain constant, the pressure change can be calculated using the relationship P1/T1 = P2/T2, where P is the pressure and T is the temperature in Kelvin. To find the final pressure, rearrange the equation to P2 = P1 * (T2/T1). First, convert the temperatures from Celsius to Kelvin by adding 273.15, which gives us T1 = 35.0 + 273.15 and T2 = -40.0 + 273.15, then plug these into the equation to solve for P2.
Calculating using the given pressures and temperature changes will give the final gauge pressure in the tires at the lower temperature.
According to Charles' Law, the pressure and temperature of a gas are directly proportional if the volume is held constant. Therefore, we can use the following formula to calculate the new gauge pressure:
P2 = P1 x (T2/T1)
Where P1 is the initial gauge pressure, T1 is the initial temperature, P2 is the final gauge pressure, and T2 is the final temperature. Plugging in the values, we get:
P2 = 2.50 x 105 N/m² x (-40.0 + 273.15)/(35.0 + 273.15)