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Question
A ballon has 5.0 g mole of helium at 7°C. Calculate
- the number of atoms of helium in the balloon
- the total internal energy of the system.
Solution
Given, the number of moles of helium = 5
T = 7°C
= 7 + 273
= 280 K
a. Hence, the number of atoms (He is monoatomic)
= Number of moles × Avogadro's number
= 5 × 6.023 × 1023
= 30.015 × 1023
= 3.0 × 1024 atoms
b. Now, average kinetic energy per molecule = `3/2 k_BT`
Here, kB = Boltzmann constant .....(It has only 3 degrees of freedom)
∴ Total energy of all the atoms = Total internal energy
= `3/2 k_B T` × number of atoms
= `3/2 xx 1.38 xx 10^-23 xx 280 xx 3.0 xx 10^24`
= `1.74 xx 10^4` J
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