Worksheet: Internal energy of Monatomic and Polyatomic Gasses

In this worksheet, we will practice calculating the division of a gas’s internal energy between translational, rotational, and vibrational energies according to its particles' degrees of freedom.

Q1:

What is the average mechanical energy of a mole of an ideal monatomic gas at a temperature of 333 K?

  • A 4 1 5 0 J
  • B 2 2 5 0 J
  • C 4 8 9 0 J
  • D 1 1 2 0 J
  • E 3 6 6 0 J

Q2:

Two monatomic ideal gases A and B are at the same temperature. 1.0 g of gas A has the same internal energy as 0.10 g of gas B.

What is the ratio of the number of moles in gas A to the number of moles in gas B?

  • A 5 1
  • B 1 1
  • C 1 0 1
  • D 3 1
  • E 2 1

What is the ratio of the atomic mass of gas A to the atomic mass of gas B?

  • A 1 2 1
  • B 3 1
  • C 5 1
  • D 2 1
  • E 1 0 1

Q3:

To give a helium atom nonzero angular momentum requires 21.2 eV of energy, meaning that 21.2 eV is the difference between the energies of helium’s ground state and of the lowest-energy state in which a helium atom has nonzero angular momentum. Find the lowest temperature at which helium atoms possess angular momentum if the energy required to give a helium atom nonzero momentum equals Boltzmann’s constant multiplied by 𝑇2.

  • A 4 . 9 2 × 1 0 K
  • B 8 . 3 1 × 1 0 K
  • C 6 . 1 7 × 1 0 K
  • D 9 . 6 4 × 1 0 K
  • E 2 . 6 6 × 1 0 K

Q4:

What is the internal energy of 6.00 mol of an ideal monatomic gas which has a temperature of 2.00×10C?

  • A 4 . 2 6 × 1 0 J
  • B 2 . 3 6 × 1 0 J
  • C 9 . 9 6 × 1 0 J
  • D 1 . 5 0 × 1 0 J
  • E 3 . 5 4 × 1 0 J

Q5:

0.82 mol of dilute carbon dioxide at a pressure of 1.80 atm occupies a volume of 58 L. What is the internal energy of the gas?

Q6:

An ideal gas at room temperature has a pressure of 0.802 atm and a volume of 13.00 L. The gas is compressed adiabatically and quasi-statically until its pressure is 3.610 atm and its volume is 5.27 L. How many degrees of freedom does the gas have?

Q7:

Calculate the internal energy of 82 g of helium at a temperature of 15C.

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