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Introduction to Flight 7th Edition by John Anderson
Edition 7ISBN: 978-0073380247Introduction to Flight 7th Edition by John Anderson
Edition 7ISBN: 978-0073380247 Exercise 2
Consider 1 kg of helium at 500 K. Assuming that the total internal energy of helium is due to the mean kinetic energy of each atom summed over all the atoms, calculate the internal energy of this gas. Note: The molecular weight of helium is 4. Recall from chemistry that the molecular weight is the mass per mole of gas; that is, 1 mol of helium contains 4 kg of mass. Also. 1 mol of any gas contains 6.02 × 10 23 molecules or atoms (Avogadro's number).
Explanation
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Verified
The mean kinetic energy of each atom is,
Here, k is the bellman constant and T is the temperature.
Substitute
for k and 500 K for T in
.
Given that,
of helium contains 4 kg of mass and
of helium gas contains
. So, 1 kg of helium gas contains one fourth of atoms. So, the number of atoms in 1 kg of helium gas is,
Here,
is the Avogadro's number.
Substitute
for
.
Total internal emery is,
Substitute
for E and
for n.
Hence, the internal energy is
.
Here, k is the bellman constant and T is the temperature.Substitute
for k and 500 K for T in . Given that, of helium contains 4 kg of mass and of helium gas contains . So, 1 kg of helium gas contains one fourth of atoms. So, the number of atoms in 1 kg of helium gas is, Here, is the Avogadro's number.Substitute
for . Total internal emery is, Substitute for E and for n. Hence, the internal energy is .
Introduction to Flight 7th Edition by John Anderson
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