Answer:
[tex]T_1 = -57.15^{\circ}C[/tex]
Explanation:
Given
[tex]P_1 = 650mmHg[/tex] --- Initial Pressure
[tex]V_1 = 5.0L[/tex] --- Initial Volume
[tex]V_2 = 5.7L[/tex] --- Final Volume
[tex]P_2 = 800mmHg[/tex] --- Final Pressure
[tex]T_2 = 30C[/tex] ---- Final Temperature
Required
Determine the initial temperature (T1)
This question will be solved using combined gas law which states:
[tex]\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}[/tex]
However, the final temperature must be converted to degree kelvin
[tex]T_2 = 30C[/tex] --- Add 273.15
[tex]T_2 = 30k + 273.15 k[/tex]
[tex]T_2 = 303.15k[/tex]
Make T1 the subject in [tex]\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}[/tex]
[tex]T_1 = \frac{P_1V_1T_2}{P_2V_2}[/tex]
Substitute values for P1, V1, T2, P2 and V2
[tex]T_1 = \frac{650 * 5.0 * 303.15}{800 * 5.7}[/tex]
[tex]T_1 = \frac{985237.5}{4560}[/tex]
[tex]T_1 = 216.060855263[/tex]
Approximate
[tex]T_1 = 216k[/tex]
Convert to degree Celsius
[tex]T_1 = 216k[/tex] --- Subtract 273.15
[tex]T_1 = 216 - 273.15[/tex]
[tex]T_1 = -57.15^{\circ}C[/tex]
Hence, the initial temperature is -57.15C
