Calculating Required Air Temperature for Hot Air Balloon Stability

[unctarheels1]

Need to see if I worked this right.
Hot air balloon floating in air has at 0 degrees C ( desnsity = 1.293kg/m^3). The mass of the balloon and passengers is 1650kg. If they want to stay at a constant height, estimate the required average temperature of the air in the balloon. Assume the volume of air in the balloon is 5000m^3 and the density of air varies with temperature according to the following information.
-10 degrees C = 1.341 kg/m^3
-5 degrees C = 1.316 kg/m^3
0 degrees C = 1.293 kg/m^3
+5 degrees C = 1.269 kg/m^3
+10 degrees C = 1.247 kg/m^3
MY SOLUTION:
B = (1.293kg/m^3)(5000m^3)(9.81m/s^2) = 63422N Buoyant Force
Weight of Balloon is (1650kg)(9.81m/s^2) = 16187N
63422N-16187N=47235N
47235N/9.81m/s^2 = 4815kg
Density of air in balloon is 4185kg/5000m^3 = .963kg/m^3
So here I would have to assume the Pressure is standard and is equal to 101325 so from row=P/RT it would give me a temp in degrees C of 93.5. I assume that pressure because it seems that was the value he used in the table to calculate the density for the temps from -10 to +10.
Have I made any mistakes? Thanks

 

[Astronuc]

That's about right. The answer may vary by +/- 1-2 K depending on the pressure, air density and gas constant used.

 

[unctarheels1]

Thanks for the response. Just worried that I made a mistake somewhere along the line of solving this problem.