Question

Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load when a balloon of radius 10 m, mass 100 kg is filled With helium at 1·66 bar at 27°C. (Density of air = 1·2 kg m^-3 and R = 0·083 bar dm³ K^–1mo1^–1).

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Solution

space Volume space of space balloon comma space space space straight V space equals space 4 over 3 πr cubed semicolon space space space straight r space equals space 10 space straight m space straight V space equals space 4 over 3 cross times space 3.14 space cross times space left parenthesis 10 space straight m right parenthesis cubed space equals space 4186.7 space straight m cubed space Mass space of space air space displaced space equals space Volume space cross times space density space space space space space space space space space space equals 4186.7 space straight m cubed space cross times space 1.2 space kg space straight m to the power of negative 3 end exponent space equals space 5024 space kg space Here space straight T space equals space 27 plus 273 space equals space 300 space straight K space space space space space space space space space PV space equals space nRT space or space straight n space equals space PV over RT

therefore space space space space straight n space equals space fraction numerator 1.66 space bar space cross times space 4186.7 space straight m cubed over denominator 0.083 space bar space dm cubed space straight K to the power of negative 1 end exponent space mol to the power of negative 1 end exponent space cross times space 300 space straight K end fraction space space space space space space space space space space space equals space 279.1 space cross times space 10 cubed space mol

therefore space space Mass space of space helium space present space space equals space 279.1 space cross times space 10 cubed space cross times space 4 space cross times space 10 to the power of negative 3 end exponent space kg space space space space space space space space space equals space 1116.4 space kg therefore space space Mass space of space filled space balloon space equals space 100 plus 1116.4 space equals space 1216.4 space kg therefore space space space Pay space load space equals space left parenthesis Mass space of space displaced space air right parenthesis space minus space left parenthesis Mass space of space balloon right parenthesis space space space space space space space space space space space space space space space space space space equals space 5024 space minus space 1216.4 space space equals space 3807.6 space kg

For Daily Free Study Material Join wiredfaculty