Argon in a rigid tank is heated from an initial state of 50 °C, 2 bar and 2m ³ to a final pressure of 8 bar. Determine the final temperature in °C to 2 decimal places.
Argon cp=0.5203 kJ/kgK cv=0.3122 kJ/kgK
To determine the final temperature of the Argon in a rigid tank, we can make use of the ideal gas law and the specific heat capacities of Argon.
The ideal gas law equation is given by:
PV = nRT
Where:
P is the pressure (in bar),
V is the volume (in m³),
n is the number of moles of the gas,
R is the specific gas constant (8.314 J/(mol·K)), and
T is the temperature (in Kelvin).
To convert the given temperatures from Celsius to Kelvin, we can use the formula:
T(K) = T(°C) + 273.15
Given:
Initial state:
T1 = 50 °C = 50 + 273.15 = 323.15 K
P1 = 2 bar
V1 = 2 m³
Final pressure:
P2 = 8 bar
We need to find the final temperature:
T2 = ?
To solve for the final temperature, we can rearrange the ideal gas law equation as:
T2 = (P2 * V1 * T1) / (P1 * V2)
First, we need to calculate the number of moles of Argon in the gas using the ideal gas law equation. Rearranging it, we have:
n = (P1 * V1) / (R * T1)
Substituting the given values:
n = (2 * 2) / (8.314 * 323.15)
Now, we can calculate the final volume of the gas by rearranging the ideal gas law equation:
V2 = (P1 * V1 * T1) / (P2 * n * R)
Substituting the given values and the calculated value of n:
V2 = (2 * 2 * 323.15) / (8 * 0.026131)
Finally, we can substitute the obtained values of V2, P2, and n into the equation for T2 to calculate the final temperature:
T2 = (P2 * V1 * T1) / (P1 * V2)
Substituting the given values:
T2 = (8 * 2 * 323.15) / (2 * 0.099085)
Evaluate the final temperature T2 to obtain the answer.