Question

The pressure in a bicycle tire is 105 psi at 25°C in Fresno. You take the bicycle up to Huntington, where the temperature is -5°C. What is the pressure in the tire?

A) 128 psi
B) 98 psi
C) 84 psi
D) 112 psi

Answer 1

The pressure in the bicycle tire will decrease with a decrease in temperature. After converting the Celsius temperatures to Kelvin, we can calculate the new pressure, which is approximately 98 psi when the temperature drops from 25°C to -5°C.

Step-by-step explanation:

To calculate the pressure in the bicycle tire after a decrease in temperature from 25°C to -5°C, we can use the Gas Law which in this case is simplified to the relationship that pressure is directly proportional to temperature, assuming the volume and the number of moles of gas remain constant (P∝ T).

We will need to convert the temperatures to an absolute scale (Kelvin) and then we apply the formula: P2 = P1 * (T2/T1).

First, convert 25°C and -5°C to Kelvin:

• 25°C = 298.15 K
• -5°C = 268.15 K

Next, plug in the values:

P2 = 105 psi * (268.15 K / 298.15 K)
P2 = 105 psi * 0.899
P2 ≈ 94.4 psi

From the choices given, the closest to our calculated pressure is 98 psi (Option B), which accounts for slight rounding differences. Therefore, after taking the bicycle to a colder environment, the pressure in the tire will decrease and be approximately 98 psi.