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Ch.5 - Gases
Chapter 5, Problem 121

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.
Express Charles's Law mathematically as V1T1=V2T2, where V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures in Kelvin.
Calculate the initial volume V1 using the formula for the volume of a cylinder: V1=πr2h1, where h1=22.6 m.
Calculate the final volume V2 using the formula for the volume of a cylinder: V2=πr2h2, where h2=23.8 m.
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 T2 in Kelvin, and convert it back to Celsius if needed.