Final answer:
To expand a gas volume from 2.8 L at 27 degrees Celsius to 15 L, the temperature must be increased to 1334.14 degrees Celsius. This is calculated using Charles's Law, which relates gas volume and temperature at constant pressure.
Step-by-step explanation:
To find the temperature needed to expand the volume of gas from 2.8 L to 15 L, we begin by using Charles's Law, which states that, at constant pressure, the volume of an ideal gas is directly proportional to its absolute temperature (in Kelvin). Charles's Law is represented by the equation V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.
First, we convert the initial temperature from Celsius to Kelvin:
T1 (in K) = 27 °C + 273 = 300 K
Then, we substitute the known values into Charles's Law equation:
(2.8 L / 300 K) = (15 L / T2)
To solve for T2, we cross-multiply and then divide:
T2 = (15 L × 300 K) / 2.8 L
T2 = 1607.14 K
Last, we convert T2 from Kelvin back to Celsius to find the needed temperature:
T2 (in °C) = 1607.14 K - 273 = 1334.14 °C
The temperature needed to expand the volume of the gas to 15 L is 1334.14 °C.