Question

He volume of an ideal gas enclosed in a thin, elastic membrane in a room at sea level with air temperature 16 °c is 0.6 m³. if the temperature of the room is increased by 24 °c, what is the new volume of the gas (in m³)?

Answer 1

Using Charles's Law, the new volume of an ideal gas when the temperature is increased from 16°C to 40°C at constant pressure is approximately 0.650 m³.

Step-by-step explanation:

To find the new volume of an ideal gas after a temperature change, we use Charles's Law. Charles's Law states that the volume of a fixed amount of gas maintained at constant pressure is directly proportional to its Kelvin temperature (V/T = constant). Therefore, we can set up a proportion.

First, convert the temperatures from Celsius to Kelvin:
Initial Temperature = 16°C = 16 + 273.15 = 289.15 K
Final Temperature = 16°C + 24°C = 40°C = 40 + 273.15 = 313.15 K

We can set up the ratio using the initial volume and temperature and the final temperature:
(V1 / T1) = (V2 / T2) where V1 is the initial volume, T1 is the initial temperature, V2 is the final volume, and T2 is the final temperature.

Plugging in the known values:
0.6 m³ / 289.15 K = V2 / 313.15 K
Solve for V2:
V2 = 0.6 m³ * (313.15 K / 289.15 K)
V2 ≈ 0.650 m³

The new volume of the gas is approximately 0.650 m³ when the temperature is increased by 24°C at constant pressure.