The objective of this problem is to determine the payload mass(i.e, basket, peop

Question

The objective of this problem is to determine the payload mass(i.e, basket, people, and ballast) which can be carried aloft by a"cold-air" balloon, which does not require a propane burner and canfunction no matter what the temperature of the ambient air. Gaseous hydrogen at ordinary temperatures and pressuresconsists of diatomic molecules (with the chemical formula H_2) forwhich M_mol = 2.016 g/mol Suppose that the balloon (fabric and lanyards) has a mass of50 kg, and that the air has a density of 1.204 kg/m^3 and atemperature of 68 degrees Fahrenheit. The balloon is filled with pure hydrogen gas and then scaledto prevent any leakage. Assume that the hydrogen achieves thermalequilibrium with the ambient air prior to the balloon ascent, andthat the hydrogen achieves a final pressure of 1.3 atm in thisstate. Given that the volume enclosed by the balloon is 750 m^3,determine: a) the mass of the hydrogen within the balloon in (kg) b) the number of hydrogen atoms within the balloon c) the density of the hydrogen within the balloon (inkg/m^3) d) the maximum payload mass which can be supported (jnkg) e) the weight associated with this payload mass (in N) I need step by step solutions for each question please.. The objective of this problem is to determine the payload mass(i.e, basket, people, and ballast) which can be carried aloft by a"cold-air" balloon, which does not require a propane burner and canfunction no matter what the temperature of the ambient air. Gaseous hydrogen at ordinary temperatures and pressuresconsists of diatomic molecules (with the chemical formula H_2) forwhich M_mol = 2.016 g/mol Suppose that the balloon (fabric and lanyards) has a mass of50 kg, and that the air has a density of 1.204 kg/m^3 and atemperature of 68 degrees Fahrenheit. The balloon is filled with pure hydrogen gas and then scaledto prevent any leakage. Assume that the hydrogen achieves thermalequilibrium with the ambient air prior to the balloon ascent, andthat the hydrogen achieves a final pressure of 1.3 atm in thisstate. Given that the volume enclosed by the balloon is 750 m^3,determine: a) the mass of the hydrogen within the balloon in (kg) b) the number of hydrogen atoms within the balloon c) the density of the hydrogen within the balloon (inkg/m^3) d) the maximum payload mass which can be supported (jnkg) e) the weight associated with this payload mass (in N) I need step by step solutions for each question please..

Explanation / Answer

a) the mass of the hydrogen within the balloon in (kg) mass=2.016*PV/RT*10-3= P=1.3 atm=1.3*105   Pa V=750 m3 T=68 F=20 0C=293 K => mass=80.7kg (b) the number of hydrogen atoms within the balloon N=2*Number of moles*Na=2*PV/RT*Na=4.8*1028 (c) the density of the hydrogen within the balloon (inkg/m^3) d=mass/V=0.11kg/m3 (d)the maximum payloadmass which can be supported payload=(1.204-0.11)*g*V -50*9.8=274 kg (e) the weightassociated with this payload mass (in N) weight=payload*g=2685 N (d)the maximum payloadmass which can be supported payload=(1.204-0.11)*g*V -50*9.8=274 kg (e) the weightassociated with this payload mass (in N) weight=payload*g=2685 N

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