A gas of volume 2m^3 at 27C is heated to 327C at constant pressure. What is its new volume?
27 C = 300 K
327 C = 600 K
temperature doubles, volume doubles
PV = n R T
V/T = constant at constant n R/P
To find the new volume of the gas, we can use Charles's Law, which states that at constant pressure, the volume of a gas is directly proportional to its temperature.
Charles's Law can be expressed using the equation:
V1 / T1 = V2 / T2
Where:
V1 is the initial volume of the gas,
T1 is the initial temperature of the gas,
V2 is the final volume of the gas (what we want to find),
T2 is the final temperature of the gas.
Given:
V1 = 2 m^3 (initial volume),
T1 = 27°C (initial temperature),
T2 = 327°C (final temperature).
To solve for V2, we rearrange the equation:
V2 = (V1 * T2) / T1
Plugging in the values:
V2 = (2 m^3 * 327°C) / 27°C
Now, let's simplify the equation:
V2 = (2 * 327) / 27 m^3
V2 = 654 / 27 m^3
The approximate value of V2 is 24.22 m^3. Therefore, the new volume of the gas is approximately 24.22 cubic meters.