Answered

Charles's law states that the volume of a gas is directly related to the absolute temperature when there is no change in the pressure or amount of gas.

Part A

A sample of gas in a balloon has an initial temperature of [tex]$7^{\circ} C$[/tex] and a volume of 1040 L. If the temperature changes to [tex]$700^{\circ} C$[/tex], and there is no change in pressure or amount of gas, what is the new volume, [tex][tex]$V$[/tex][/tex], of the gas?

Express your answer with the appropriate units.

[tex]\frac{V_1}{T_1} = \frac{V_2}{T_2}[/tex]



Answer :

GinnyAnswer
Sure, let's solve the problem step-by-step using Charles's Law which is given by [tex]\(\frac{V_1}{T_1} = \frac{V_2}{T_2}\)[/tex]. Charles's Law states that the volume of a gas is directly proportional to its temperature when the pressure and the amount of gas are held constant. Here are the steps to determine the new volume [tex]\(V_2\)[/tex]:

1. Convert the initial and final temperatures from Celsius to Kelvin:
- Initial temperature [tex]\(T_1 = 7^{\circ} C\)[/tex]. To convert this to Kelvin, add 273.15.
[tex]\[ T_1 = 7 + 273.15 = 280.15 \text{ K} \][/tex]
- Final temperature [tex]\(T_2 = 700^{\circ} C\)[/tex]. To convert this to Kelvin, add 273.15.
[tex]\[ T_2 = 700 + 273.15 = 973.15 \text{ K} \][/tex]

2. Use Charles's Law to find the final volume [tex]\(V_2\)[/tex]:
- The initial volume [tex]\(V_1\)[/tex] is given as 1040 L.
- Charles's Law formula is [tex]\(\frac{V_1}{T_1} = \frac{V_2}{T_2}\)[/tex]. Rearranging to solve for [tex]\(V_2\)[/tex]:
[tex]\[ V_2 = V_1 \times \frac{T_2}{T_1} \][/tex]
- Plugging in the known values:
[tex]\[ V_2 = 1040 \times \frac{973.15}{280.15} \][/tex]
- Calculate [tex]\(V_2\)[/tex]:
[tex]\[ V_2 \approx 1040 \times 3.474 = 3612.62 \text{ L} \][/tex]

The new volume [tex]\(V_2\)[/tex] is approximately 3612.62 liters.