Question

the inside of a basketball has a pressure of 0.476 atm at 25.0°c. what is the pressure inside of the ball if the temperature is decreased to 20.0°c? use the formula: \\(\frac{p_1}{t_1} = \frac{p_2}{t_2}\\)

Explanation:

Step1: Convert temperatures to Kelvin

To use the gas law formula, we need to convert Celsius temperatures to Kelvin. The conversion formula is \( T(K) = T(^\circ C) + 273.15 \).

For \( T_1 \): \( T_1 = 25.0 + 273.15 = 298.15 \, K \)

For \( T_2 \): \( T_2 = 20.0 + 273.15 = 293.15 \, K \)

Step2: Rearrange the formula to solve for \( P_2 \)

Given \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \), we can rearrange it to \( P_2 = P_1 \times \frac{T_2}{T_1} \)

Step3: Substitute the known values

We know \( P_1 = 0.476 \, atm \), \( T_1 = 298.15 \, K \), and \( T_2 = 293.15 \, K \). Substituting these values into the formula:

\( P_2 = 0.476 \, atm \times \frac{293.15 \, K}{298.15 \, K} \)

First, calculate the ratio \( \frac{293.15}{298.15} \approx 0.9832 \)

Then, multiply by \( P_1 \): \( P_2 = 0.476 \times 0.9832 \approx 0.468 \, atm \)

Answer:

The pressure inside the ball at \( 20.0^\circ C \) is approximately \( \boldsymbol{0.468 \, atm} \)