A gas at a temperature of 600C and 1ATM has a volume of 120 L. So what is the volume of the gas at a temperature of 400C at a constant pressure ?
To find the volume of a gas at a different temperature but constant pressure, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas (in this case, 1 ATM)
V is the volume of the gas (initially given as 120 L)
n is the number of moles of the gas (which is not given, but is constant in this case)
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature of the gas measured in Kelvin (K = °C + 273.15)
First, let's convert the temperatures to Kelvin:
For the initial temperature of 600°C:
T1 = 600 + 273.15 = 873.15 K
For the final temperature of 400°C:
T2 = 400 + 273.15 = 673.15 K
Now we can set up the equation and solve for the final volume (V2):
P1V1/T1 = P2V2/T2
Substituting the given values into the equation:
(1 ATM)(120 L) / (873.15 K) = (1 ATM)(V2) / (673.15 K)
Now, isolate V2:
V2 = [(1 ATM)(120 L) / (873.15 K)] × (673.15 K) / (1 ATM)
V2 ≈ 88.45 L
Therefore, the volume of the gas at a constant pressure of 1 ATM and a temperature of 400°C would be approximately 88.45 L.