Question

В цилиндрическом сосуде с внутренним диаметром 0.6 м и высотой 2.4 м находится воздух при температуре 18°C . Давление по манометру 0.765 МПа, а барометрическое давление 101858 Па. Найти массу воздуха в сосуде. Ответ: 7.1 кг

Answer 1

PV=mRT/μ, P=P1+Pатм, V=πd^2h/4
m=Pπd^2hμ/4RT=((0.765+0,101858)Па*3,14*0,36м^2*2,4м*29*10^-3кг/моль)/(4*8,31 Дж/К*моль*291К)≈7,1 кг (7,05 кг)

Answer 2

To find the mass of air in the cylindrical vessel, we can use the ideal gas law equation, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

Given information:

- Internal diameter of the vessel: 0.6 m - Height of the vessel: 2.4 m - Temperature of the air: 18°C (which is 18 + 273.15 = 291.15 K in Kelvin) - Pressure according to the manometer: 0.765 MPa - Barometric pressure: 101,858 Pa

Calculating the volume of the vessel:

The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius and h is the height. Since we are given the diameter, we need to divide it by 2 to get the radius.

Given: - Diameter = 0.6 m - Height = 2.4 m

Calculations: - Radius = Diameter / 2 = 0.6 / 2 = 0.3 m - Volume = π * (0.3)^2 * 2.4 = 0.678 m^3

Calculating the number of moles of air:

To find the number of moles, we need to rearrange the ideal gas law equation to solve for n:

n = PV / RT

Given: - Pressure = 0.765 MPa = 0.765 * 10^6 Pa - Volume = 0.678 m^3 - Temperature = 291.15 K - Ideal gas constant (R) = 8.314 J/(mol·K)

Calculations: - n = (0.765 * 10^6 * 0.678) / (8.314 * 291.15) = 0.0339 moles

Calculating the mass of air:

To find the mass of air, we need to multiply the number of moles by the molar mass of air. The molar mass of air is approximately 28.97 g/mol.

Given: - Number of moles = 0.0339 moles - Molar mass of air = 28.97 g/mol

Calculations: - Mass = 0.0339 * 28.97 = 0.981 g = 0.981 / 1000 = 0.981 kg

Therefore, the mass of air in the cylindrical vessel is approximately 0.981 kg.