Temperature and Ideal Gases

Question 1

Define thermal energy

Answer 1

Thermal energy is the transfer of energy from a region of higher temperature to a region of lower temperature.

Question 2

Is temperature a base quantity?

Answer 2

Yes

Question 3

Explain thermal equilibrium

Answer 3

Two systems in thermal contact are said to be in thermal equilibrium if there is no net exchange of thermal energy between them.

Question 4

What are the two types of temperature scales?

Answer 4

Empirical scale and centigrade scale

Question 5

How can you find temperature using the Centigrade scale?

Answer 5

t = (Xt - X100)/(Xt - X0) * 100%

Question 6

What is the ideal gas equation?

Answer 6

pV = nRT / pV = NkT

Question 7

Conversion rate between T/K and T/C

Answer 7

T/K = T/C + 273.15

Question 8

Define internal energy

Answer 8

Internal energy U of a system is the sum of the random distribution of kinetic Ek and potential Ep energies associated with the molecules in the system

Question 9

In a solid, how are the molecules like?

Answer 9

The molecules are confined to their lattice positions and undergo only vibrational motion
about these fixed positions, giving rise to vibrational kinetic energies.
The molecules are close to each other and thus have high potential energy.

Question 10

In a liquid, how are the molecules like?

Answer 10

The molecules are not fixed in position and have more degrees of freedom, i.e. they can
undergo vibrational, translational and rotational motion, giving rise to higher kinetic
energies.
The average intermolecular separation is larger than in the solid state, as the molecules
can move randomly. The larger intermolecular separation results in weaker intermolecular forces and hence less significant molecular potential energy.

Question 11

In a gas, how are the molecules like?

Answer 11

The molecules are spread. Like in the liquid state, they can also undergo vibrational,
translational and rotational motion, giving rise to high kinetic energies.
The average intermolecular separation is larger than in liquid or solid. This results in much
weaker intermolecular forces and the least amount of potential energy among the three
states.

Question 12

How does a gas behave like a certain gas?

Answer 12

When gases are at very low pressure, the gas molecules are very far apart
from each other. And when gases are at very high temperature, the gas molecules have
significantly high kinetic energy. Under such conditions, the gas will have negligible
microscopic potential energy and will behave like an ideal gas.

Question 13

Definition of a mole

Answer 13

One mole, n, is the amount of substance that contains as many particles as there are atoms
in 0.0120 kg of carbon-12, which is 6.02 * 10^23 particles.

Question 14

Define the Avogadro’s constant

Answer 14

The Avogadro’s constant, NA, is defined as the number of atoms in 0.0120 kg of carbon-12,
which is 6.02 * 10^23 mol–1

Question 15

What are the formulae to find the number of moles of a substance?

Answer 15

n = N/Na (N = total number of particles/molecules/atoms, Na = 6.02 * 10^23 mol–1)

n = Nm(molecule) / Mr (N = total number of particles/molecules/atoms, m(molecule) = molecular mass, Mr = molar mass of gas)

n = M/Mr(N = total number of particles/molecules/atoms, M = total mass of substance, Mr = Mr = molar mass of gas)

Question 16

Formula for Boltzmann’s constant, k

Answer 16

k = R/Na
R (given in ideal gas formula) Na (Avogadro’s constant)

Question 17

What are the 6 basic assumptions of kinetic theory of gases?

Answer 17

1. A gas consists of a very large number of molecules.
2. The molecules are in constant, random motion and obey Newton’s laws of motion.
3. Collision between gas molecules are elastic.
4. Collision between gas molecules and the walls of the container are elastic.
5. Intermolecular force only act during collisions between molecules. The duration of a collision is negligible compared with the time interval between collisions.
6. The volume of the gas particles themselves is negligible compared with the volume
   occupied by the gas.

Question 18

Find the pressure (cx is the velocity constant, Distance to wall = x)

Answer 18

Final momentum - Initial momentum = (-mcx) - (mcx) = -2mcx

Time interval = 2l/cx

Average force = Change in momentum/Time interval = -2mcx/(2l/cx) = -mcx^2/l

Newton’s 3rd law of motion: Fave = mcx^2/l

Total force = m/l(cx1^2 + cx2^2 +… cxn^2)
= Nm/l * <cx^2>

Pressure = (Nm/l * <cx^2>) / l^2 = Nm<cx^2> / l^3 = Nm<cx^2>/V (V = l^3, volume of container)

<cx^2> + <cy^2> + <cz^2> = <c^2>
<cx^2> = <cy^2> = <cz^2>
3<cx^2> = <c^2>

Pressure = Nm<c^2> / 3V = (1/3 *Nm<c^2>) / V

Question 19

Relationship between thermodynamic temperature and mean kinetic energy of a molecule

Answer 19

pV = 1/3 Nm<c^2>
NkT = 1/3 Nm<c^2>
3/2 kT = 1/2 m<c^2>
3/2kT = Ek

<Ek> proportional to T
</Ek>

Question 19

A rise in temperature gives a ? to internal energy.

Answer 19

Rise

Question 20

Internal energy formula

Answer 20

U = N<Ek>
U = 3/2 NkT
U = 3/2 nRT</Ek>