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.
