Answer:
[tex]\boxed {\boxed {\sf 8.38 \ L}}[/tex]
Explanation:
We are asked to find the new volume of a gas after a change in temperature. We will use Charles's Law, which states the volume of a gas is directly proportional to the temperature. The formula for this law is:
[tex]\frac {V_1}{T_1}= \frac{V_2}{T_2}[/tex]
The gas starts at 100 degrees Celsius and a volume of 33.5 liters. Substitute these values into the formula.
[tex]\frac {33.5 \ L}{100 \textdegree C}=\frac{ V_2}{T_2}[/tex]
The gas is cooled to 25 degrees Celsius, but the volume is unknown.
[tex]\frac {33.5 \ L}{100 \textdegree C}=\frac{ V_2}{25 \textdegree C}[/tex]
We want to find the volume of the gas after it is cooled. We must isolate the variable V₂. It is being divided by 25 degrees Celsius and the inverse of division is multiplication. Multiply both sides of the equation by 25 °C.
[tex]25 \textdegree C*\frac {33.5 \ L}{100 \textdegree C}=\frac{ V_2}{25 \textdegree C}* 25 \textdegree C[/tex]
[tex]25 \textdegree C*\frac {33.5 \ L}{100 \textdegree C}= V_2[/tex]
The units of degrees Celsius cancel.
[tex]25*\frac {33.5 \ L}{100 }= V_2[/tex]
[tex]8.375 \ L = V_2[/tex]
The original measurements have 3 significant figures, so our answer must have the same. For the number we found, that is the hundredth place. The 5 in the thousandths place tells us to round the 7 up to an 8.
[tex]8.38 \ L \approx V_2[/tex]
The new volume after the gas is cooled is approximately 8.38 liters.
