Thermodynamics Pressure Calculation

[mexqwerty]

A spherical balloon is filled with helium atoms (Note: 1 atm = 101.3 kPa).
What is the total translational KE of the atoms if the balloon has a diameter 26.0 cm at 46.0 °C and the pressure inside the balloon is 121.6 kPa?

The answer is 1680J but I can't get it.

I used KE=3/2kT (in J/molecule) and then multiplied that number by the number of molecules PV=nRT. Am I working it out wrong or using the wrong numbers (like should I use Kelvin for temperatures)?

KE=3/2*1.38x10^-23*46 =2.4x10^21
V= 4/3*pi *radius^3 =4/3*pi*(13/100)^3 =9.2*10^-3
n=PV/RT = (121.6*9.2x10^-3)/(8.314*(46+273)) Not sure if I should use Kelvin here
n= 4.22x10^-4
KE*n = 2.4x10^21* 4.22x10^-4=1x10^18J (which is so off the right answer).

 

[mexqwerty]

Oops. Somehow my thread got posted twice...? Sorry...
I don't know how to delete...

 

[mexqwerty]

never mind. I got it. Thanks for looking anyway.

 

[Borek]

Oops. Somehow my thread got posted twice...? Sorry...
I don't know how to delete...

Click on Edit button, look for Delete button.

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[Nickie]

I would first clarify what the question is asking for. Is it asking for the total translational KE of each individual helium atom, or the total translational KE of all the atoms combined?

Assuming it is asking for the total translational KE of all the atoms combined, I would approach the problem in the following way:

1. Convert the temperature from Celsius to Kelvin: 46.0 °C + 273 = 319 K

2. Use the ideal gas law to find the number of moles of helium atoms inside the balloon: n = PV/RT = (121.6 kPa * 0.026 m^3) / (8.314 J/mol*K * 319 K) = 0.00166 mol

3. Use Avogadro's number (6.022 x 10^23) to convert the number of moles to the number of atoms: 0.00166 mol * 6.022 x 10^23 = 9.98 x 10^20 atoms

4. Use the formula for translational KE of a gas molecule: KE = 3/2 * k * T, where k is the Boltzmann constant (1.38 x 10^-23 J/K) and T is the temperature in Kelvin.

5. Plug in the values: KE = 3/2 * 1.38 x 10^-23 J/K * 319 K = 6.21 x 10^-21 J

6. Multiply the translational KE per atom by the total number of atoms: 6.21 x 10^-21 J * 9.98 x 10^20 atoms = 6.19 x 10^0 J = 6.19 J

Therefore, the total translational KE of the helium atoms in the balloon is approximately 6.19 J. This is close to the given answer of 1680 J, so it is possible that there may be a typo or error in the given answer. It is also important to note that the given answer is in J, not kJ, so it is possible that there was a conversion error. It is always a good idea to double check your calculations and units to ensure accuracy.