A convenient and cost-effective way to store biogas is to use light-weight, rigid gas containers. The pressure and temperature of biogas stored in a 10 m^3 container are 1.5 bar and 5°C, respectively, as measured at an early morning time (state 1). The temperature of the biogas is expected to increase to 40°C at noon on the same day, without any significant change in the volume of the container or amount of methane in the container (state 2). The biogas can be approximated as methane (CH4) modelled as an ideal gas with constant specific heat ratio, k = 1.4. The effects of gravity and motion are negligible. The reference environment pressure and temperature are, respectively, po = 100 kPa and To = 0 °C. The molecular weight of methane is M = 16.04 gmol-1. The universal gas constant is R = 8.31 J mol-1K-1. (a) Calculate the mass, in kg, and amount of substance, in mol, for the methane in the container.

Question

Engineering

Fritz

8 June, 20:31

A convenient and cost-effective way to store biogas is to use light-weight, rigid gas containers. The pressure and temperature of biogas stored in a 10 m^3 container are 1.5 bar and 5°C, respectively, as measured at an early morning time (state 1). The temperature of the biogas is expected to increase to 40°C at noon on the same day, without any significant change in the volume of the container or amount of methane in the container (state 2). The biogas can be approximated as methane (CH4) modelled as an ideal gas with constant specific heat ratio, k = 1.4. The effects of gravity and motion are negligible. The reference environment pressure and temperature are, respectively, po = 100 kPa and To = 0 °C. The molecular weight of methane is M = 16.04 gmol-1. The universal gas constant is R = 8.31 J mol-1K-1. (a) Calculate the mass, in kg, and amount of substance, in mol, for the methane in the container.

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Answers (1)

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Mueller · Answer 1

10.41 kg

Explanation:

The gas state equation is:

p * V = n * R * T

For this equation we need every value to be in consistent units

1.5 bar = 150 kPa

5 C = 278 K

n = p * V / (R * T)

n = 150000 * 10 / (8.31 * 278) = 649 mol

Multiplying the amount of moles by the molecular weight of the gas we obtain the mass:

m = M * mol

m = 16.04 * 649 = 10410 g = 10.41 kg