To solve this problem, we can use the ideal gas law, which states:
PV = nRT
Where: P = Pressure (in Pa) V = Volume (in m³) n = Number of moles R = Gas constant (in J/(mol·K)) T = Temperature (in Kelvin)
First, we need to convert the given temperatures from Celsius to Kelvin: T1 = 50°C + 273.15 = 323.15 K T2 = 30°C + 273.15 = 303.15 K
Next, we can calculate the initial and final number of moles of gas using the ideal gas law equation:
n1 = (P1 * V) / (R * T1) n2 = (P2 * V) / (R * T2)
Given: P1 = 20000 kPa = 20000 * 1000 Pa P2 = 5000 kPa = 5000 * 1000 Pa V = 30 liters = 0.03 m³ R = 0.29 kJ/(kg·K) = 0.29 * 1000 J/(kg·K) = 290 J/(kg·K)
Substituting the values:
n1 = (20000 * 1000 * 0.03) / (290 * 323.15) n2 = (5000 * 1000 * 0.03) / (290 * 303.15)
Now, we can calculate the difference in the number of moles:
Δn = n2 - n1
Finally, we can calculate the mass of the gas released using the molecular weight (M) of the gas:
Mass = Δn * M
Since you haven't specified the gas being used, I'll assume it is an ideal gas with a molecular weight of 28.97 g/mol, which corresponds to the average molecular weight of air.
M = 28.97 g/mol = 0.02897 kg/mol
Substituting the values and calculating:
Δn = ((5000 * 1000 * 0.03) / (290 * 303.15)) - ((20000 * 1000 * 0.03) / (290 * 323.15)) Mass = Δn * 0.02897
By evaluating these equations, you can determine the mass of gas released in kilograms.