Helium balloon problem adiabatic process

[kellya55]

Homework Statement

A large research balloon containing 2000 m^3 of helium gas at 1.00 atm and a temperature of 15.0 celsius rises rapidly from ground level to an altitude at which the atmospheric pressure is only 0.900 atm (the figure (Figure 1) ). Assume the helium behaves like an ideal gas and the balloon's ascent is too rapid to permit much heat exchange with the surrounding air.Calculate the volume of the gas at the higher altitude?Calculate the temperature of the gas at the higher altitude?

Homework Equations

Adiabatic process

T1V1^gamma-1=T2V2^gamma-1 where gamma is 1.67 for helium

The Attempt at a Solution

Found volume of helium to be 2130 m ^3 which was correct but then kept on getting a temperature of around 3.-3.3 celsius(answer is to be given in celsius)using different vales for atm and gamma.It says that my rounding is off so I'll give step by step procedure of what I did
288.15 x 2000^0.67=T2 x 2130^0.67
and T2=276.24 and 276.24-273.15 is 3.1 celsius to 2 significant figures please help!

 

[ehild]

The temperature can be obtained easier (and with less error) using the ideal gas law:

PV/T=const.

The value for the new temperature is 3.1 °C.
ehild