Chapter 8: Temperature & Ideal Gases

Question 1

State what is meant by an ideal gas.

Answer 1

A gas that obeys the equation pV = nRT for all values of P, V and T for a fixed amount n of gas.

Question 2

Define thermal equilibrium

Answer 2

When there is no net exchange of energy between two bodies placed in thermal contact and temprature is same between two bodies

Question 3

How to convert K into °C?

Answer 3

K = θ + 273.15

Question 4

State the Ideal Gas equation

Answer 4

pV = nRT where n = number of mols
OR
pV = NkT where N = number of particles

Question 5

State any 2 assumptions of the kinetic theory of gases

Answer 5

1. Any gas is made up of a large number of particles
2. The particles are in constant and random motion
3. There is no gain or loss in KE when particles collide
4. The volume of each particle is negligible compared to the volume of the gas
5. The forces between particles are negligible except during time of collision
6. Duration of collisions is negligible compared to time interval between collisions

Question 6

Derive the equation pV = ⅓Nm<c²>

Answer 6

1. Change in momentum of partcle = -2mcₓ
2. Time taken to travel = (distance / speed) = 2L / cₓ
3. Force of wall on particle
   = Rate of change of momentum
   = - (2mcₓ²) / (2L)
   = - (mcₓ²) / L
   Force of particle on wall = (mcₓ²) / L
4. Since Pressure = (Force / Area),
   Pressure = m(c1x² + c2x² + c3x² + … + cnx²) / (L^3)
5. <cx²> = (c1² + c2² + c3² + … + cn²) / N
   Pressure = (mN<c²>) / (L^3)
6. Since <cx²> = ⅓<c²>,
   pV = ⅓Nm<c²>

Question 7

State the formula of the KE of an ideal gas particle

Answer 7

E = 3/2 NkT where N = no. of particles
= 3/2 nRT where n = no. of molecules

Question 8

Explain why the internal energy of an ideal gas is proportional to its thermodynamic temperature

Answer 8

As an ideal gas does not have intermolecular forces, it thus has a molecular potential energy of zero, such that its total internal energy is due to the total kinetic energy of its molecules.
Hence, the average kinetic energy of the molecules, and thus the internal energy of the ideal gas in a system is proportional to its thermodynamic temperature.

Question 9

State two advantages of using the continuous flow method in the determination of specific heat capacity of water.

Answer 9

1. At steady state, none of the electrical energy supplied is used to warm the apparatus. As such heat capacity of the apparatus is not required in the determination of the specific heat capacity of the liquid.
2. As the temperature of the apparatus in excess of the surrounding when obtaining the two sets of data remains the same, by Newton’s Law of Cooling, the rate of heat loss to the surrounding is the same for both cases. Since
   power supplied by heater = power used to heat liquid + rate of heat loss for
   both cases, rate of heat loss can be easily eliminated by algebraic manipulation (in the calculation). Therefore the rate of overall heat loss need not be known.

Question 10

Using the kinetic model for matter, explain how heat is lost through evaporation, Hence explain how adding a lid will prevent this loss

Answer 10

Some molecules of the liquid have higher kinetic energy (KE) than others. A very fast moving molecule (i.e. with large KE) near the surface of the liquid may have enough energy to overcome the attractive forces of the neighbouring molecules and leave the liquid. As the more energetic molecules escape from the surface of the liquid, the remaining molecules in the liquid will have smaller kinetic energy. The overall K.E. of the remaining liquid molecules decreases and cooling occurs. By adding a lid, the energetic molecules that have escaped from the liquid will be confined to the space above the liquid. Some of these energetic molecules will enter the liquid as other molecules escape from the liquid. The net change in KE is zero and hence cooling does not occur

Question 11

Using the kinetic model of gases, explain how gases exert a pressure on the sides of its
container.

Answer 11

When the molecules collide with the wall, the wall exerts a force on the molecule causing the molecule to experience a change in momentum, hence it rebounds. By N3L, it exerts a force of the same magnitude back on the wall. As there are many molecules moving about randomly, colliding with the wall, an average constant force and hence pressure is exerted on the wall

Question 12

Explain an evidence provided by the photoelectric effect experiment for the failure of the wave theory of light.