Question

1. the combined gas law is an important concept in refrigeration and heating. consider 1.50 l of gas at 215 psi at 19.2°c that is expanded to 8.50 l at a pressure of 35.5 psi. what will the temperature be following the expansion?

Explanation:

Step1: Convert Celsius to Kelvin

The formula for converting Celsius to Kelvin is \(T(K)=T(^{\circ}C)+273.15\).
For the initial temperature \(T_1 = 19.2^{\circ}C\), then \(T_1=19.2 + 273.15=292.35\space K\)

Step2: Use the combined gas law formula

The combined gas law is \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\).
We need to solve for \(T_2\), so \(T_2=\frac{P_2V_2T_1}{P_1V_1}\)
Given \(P_1 = 215\space psi\), \(V_1=1.50\space L\), \(T_1 = 292.35\space K\), \(P_2=35.5\space psi\), \(V_2 = 8.50\space L\)
Substitute the values into the formula:
\(T_2=\frac{35.5\times8.50\times292.35}{215\times1.50}\)
First, calculate the numerator: \(35.5\times8.50\times292.35=(35.5\times8.50)\times292.35 = 301.75\times292.35\approx88225.16\)
Then, calculate the denominator: \(215\times1.50 = 322.5\)
\(T_2=\frac{88225.16}{322.5}\approx274\space K\)
Convert back to Celsius: \(T_2=274 - 273.15 = 0.85^{\circ}C\)

Answer:

\(0.85^{\circ}C\)