An air tank with a volume of 20m^3 is pressurized to 10 MPa. The tank eventually reaches room temperature of 25 degree C. If the air inside is allowed to escape without any heat transfer to the environment unit reaches a pressure of 200 KLPa, find the remaining mass of air in the tank and its temperature.
In the USA, it is customary to call the subject thermodynamics. Without the "s", the word "thermodynamic" is an adjective.
It may be different in some English speaking countries.
I do not recognize the meaning of "L" in KLPa. Do you mean KPa? (kiloPascals?)
The air inside undergoes an isentropic adiabatic expansion, and it cools off in the process. You will need to make use of the fact that the specific heat ratio (gamma = Cp/Cv) for air is 1.40.
P/(density)^1.4 is constant in the expansion process. If the pressure falls by a factor of 50, from 10 MPa to 0.2 MPa, the density decreases by a factor 50^(5/7) = 16.35
The new temperature can be deduced using the ideal gas law.
P/(density*T) = constant
T2/T1 = (P2/P1)*(density1/density2)
= (1/50)*(16.35) = 0.327
Temperature must be in Kelvin.
T2 = 130 K
Get the final mass in the tank from the final density and the volume.
To find the remaining mass of air in the tank and its temperature, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature
First, let's calculate the initial number of moles of air in the tank using the initial conditions:
P1 = 10 MPa = 10 * 10^6 Pa (convert MPa to Pa)
V = 20 m^3
R = 8.314 J/(mol·K) (ideal gas constant)
n1 = (P1 * V) / (R * T1)
where T1 is the initial temperature. Since the volume and pressure remain constant when the air escapes, we can assume that the number of moles also remains constant.
Now, let's calculate the final number of moles of air when the pressure reaches 200 kPa (convert kPa to Pa):
P2 = 200 kPa = 200 * 10^3 Pa
n2 = n1 (since the number of moles remains unchanged)
Finally, we can calculate the remaining mass of air using the molar mass of air (approximately 28.97 g/mol) and the number of moles:
mass = n2 * molar mass of air
To find the temperature of the remaining air, we'll rearrange the ideal gas law equation:
T2 = (P2 * V) / (n2 * R)
Now we have all the equations we need to solve the problem. Plug in the given values for pressure, volume, and initial temperature to find the initial number of moles (n1), then use the final pressure to find the final number of moles (n2). Finally, calculate the remaining mass using n2 and the molar mass of air, and find the temperature using the final pressure and volume.
Note: Remember to convert units to the appropriate ones in SI (International System of Units) before performing the calculations. Also, ensure that the temperature is given in Kelvin (K) for accurate results.