Determine the temperature on the second day, assuming that the pressure and amount of gas in a natural gas storage tank have not changed, where the tank is a cylinder with a moveable top and a fixed radius. The height of the cylinder is 22.6 m at 22 °C, and the next day the height increases to 23.8 m due to a heat wave.

Verified step by step guidance

1. Identify the relationship between the volume of the gas and temperature using Charles's Law, which states that the volume of a gas is directly proportional to its temperature when pressure and the amount of gas are constant.
2. Express Charles's Law mathematically as \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \), where \( V_1 \) and \( V_2 \) are the initial and final volumes, and \( T_1 \) and \( T_2 \) are the initial and final temperatures in Kelvin.
3. Calculate the initial volume \( V_1 \) using the formula for the volume of a cylinder: \( V_1 = \pi r^2 h_1 \), where \( h_1 = 22.6 \) m.
4. Calculate the final volume \( V_2 \) using the formula for the volume of a cylinder: \( V_2 = \pi r^2 h_2 \), where \( h_2 = 23.8 \) m.
5. Convert the initial temperature from Celsius to Kelvin by adding 273.15 to 22 °C, then use Charles's Law to solve for the final temperature \( T_2 \) in Kelvin, and convert it back to Celsius if needed.