Let us solve this problem step-by-step:
1. Identify the given values:
- Initial volume ([tex]\(V_1\)[/tex]) = 500 cm³
- Initial temperature ([tex]\(T_1\)[/tex]) = 27°C
- Final temperature ([tex]\(T_2\)[/tex]) = 277°C
2. Convert the temperatures to Kelvin:
- To convert from Celsius to Kelvin, we add 273.15.
- [tex]\(T_1\)[/tex] in Kelvin = 27 + 273.15 = 300.15 K
- [tex]\(T_2\)[/tex] in Kelvin = 277 + 273.15 = 550.15 K
3. Use Charles's Law:
- Charles's Law states that for a given amount of gas at constant pressure, the volume of the gas is directly proportional to its absolute (Kelvin) temperature. The law can be expressed as:
[tex]\[
\frac{V_1}{T_1} = \frac{V_2}{T_2}
\][/tex]
- Here, [tex]\(V_2\)[/tex] is the final volume we need to find.
4. Rearrange the formula to solve for [tex]\(V_2\)[/tex]:
[tex]\[
V_2 = \frac{T_2}{T_1} \times V_1
\][/tex]
5. Substitute the known values into the equation:
[tex]\[
V_2 = \frac{550.15 \text{ K}}{300.15 \text{ K}} \times 500 \text{ cm}³
\][/tex]
6. Calculate the final volume ([tex]\(V_2\)[/tex]):
[tex]\[
V_2 \approx 916.4584374479427 \text{ cm}³
\][/tex]
Therefore, the volume that the gas will occupy at 277°C (with the pressure kept constant) is approximately [tex]\(916.46\)[/tex] cm³.
