A gas of volume 2m^3 at 27C is heated to 327C at constant pressure. What is its new volume?
To find the new volume of the gas, we can use the ideal gas law, which states:
PV = nRT
Where:
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles of gas,
R is the ideal gas constant, and
T is the temperature of the gas in Kelvin.
First, let's convert the given temperatures into Kelvin. To convert Celsius to Kelvin, we use the formula:
T(K) = T(C) + 273.15
So, the initial temperature, 27°C, becomes:
T1 = 27 + 273.15 = 300.15 K
And the final temperature, 327°C, becomes:
T2 = 327 + 273.15 = 600.15 K
Since the pressure of the gas is constant, we can rewrite the ideal gas law as:
V1/T1 = V2/T2
Now, let's plug in the values we have:
2 m^3 / 300.15 K = V2 / 600.15 K
To solve for V2, we can cross multiply and divide:
V2 = (2 m^3 * 600.15 K) / 300.15 K
V2 = 4 m^3
Therefore, the new volume of the gas after being heated to 327°C at constant pressure is 4 m^3.