Question

Neon gas (a monatomic gas) and hydrogen gas (a diatomic gas) are both held at constant volume in separate containers. Each container contains the same number of moles n of each gas. You find that it takes an input of 300 J of heat to increase the temperature of the hydrogen by 2.50°C.

Part A

How many modes does a single hydrogen gas molecule have? (Assume the vibrational modes are "frozen out").

3, all rotational kinetic

6, 3 translational kinetic and 3 rotational kinetic

2, all rotational kinetic

3, all translational kinetic

5, 3 translational kinetic and 2 rotational kinetic

Part B

Use your answer to part A) and the expression for the internal energy of a gas to find the number of moles in the gas.

n   =

?

moles

Part C

If you transfer the same amount of heat (300 J) into the container of neon (which has the same number of moles as the hydrogen container), how will the temperature change in the neon gas compare to the temperature change in the hydrogen gas?

They will be the same, because they both contain the same number of moles.

The neon will change temperature by less, because hydrogen molecules have less mass than neon molecules.

The neon will change temperature by less, because neon has more modes than hydrogen.

The neon will change temperature by less, because neon has less modes than hydrogen.

They will be the same, because they both gained the same amount of heat energy.

The neon will change temperature by more, because neon has more modes than hydrogen.

The neon will change temperature by more, because neon has less modes than hydrogen.

Part D

Solve for the numerical value of the temperature increase of the neon gas if you transfer 300 J of heat. Check that you answer matches with part C)!

Δ TNe   =

?

   ∘C

Answer 1

(A) It will be three translational (motion along x,y,z) and 2 rotational (rotation about two axes perpendicular to the axis of molecule

(B) Accroding to equipartition of energy, each degree of freedom has 0.5kT hence for 5 degree of freedom have

(C) Neon has high raise in temperature as it has Less degree of freedon or modes

(d) Molar heat capacity at constant volme for H2 will be

While for Neon, it will be

Let the raise in temperature of Hydroge is then