I am trying to solve the problem:
What is the lifting force of in kN for a 10 m diameter spherical balloon with helium inside at 101 kPa and 320 K surrounded by air at 101 kPa and 298.15 K?
The given answer is 5.28 kN.
I start from the Buoyancy Formula:
$$F_{b} = (p_{air} - p_{gas})*g*V$$
And Ideal Gas Law: $$PV = mRT$$ $$P/RT = m/V$$
Density of air: $101/0.287*298.15=1.18$
Density of He: $101/0.287*320=1.10$
Volume of helium balloon: $(4\pi/3)*(10/2)^3=(500/3\pi)$
Substitute:
$$F_b = (1.18 - 1.10)*9.81*(500/3\pi)$$
I get 0.4101 N; am I missing something or is the given answer wrong?