# 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?

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
• B
• C
• D
• E

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

• A
• B
• C
• D
• E

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 .

• A K
• B K
• C K
• D K
• E K

Q4:

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

• A J
• B J
• C J
• D J
• E 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 .