Question

the combined gas law is an important concept in refrigeration and heating. part a consider 1.17 l of gas at 255 psi at 12.1 °c that is expanded to 7.28 l at a pressure of 31.6 psi. what will the temperature be following the expansion? express the temperature in degrees celsius as an integer temperature = °c

Explanation:

Step1: Convert Celsius to Kelvin

$T_1 = 12.1+273.15 = 285.25$ K

Step2: Write the combined - gas law formula

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$

Step3: Rearrange the formula to solve for $T_2$

$T_2=\frac{P_2V_2T_1}{P_1V_1}$

Step4: Substitute the given values

$P_1 = 255$ psi, $V_1 = 1.17$ L, $T_1 = 285.25$ K, $P_2 = 31.6$ psi, $V_2 = 7.28$ L
$T_2=\frac{31.6\times7.28\times285.25}{255\times1.17}$
$T_2=\frac{31.6\times7.28\times285.25}{298.35}$
$T_2=\frac{31.6\times2076.62}{298.35}$
$T_2=\frac{65621.192}{298.35}$
$T_2 = 219.94\approx220$ K

Step5: Convert Kelvin to Celsius

$T = 220 - 273=- 53$ °C

Answer:

$-53$