9. Thermodynamics

Question 1

What is specific heat capacity?

Answer 1

• The amount of energy required to increase the temperature of 1kg of a substance by 1⁰C.
• without changing its state.

Question 2

What is specific heat capacity?

Answer 2

• The amount of energy required to change the state of 1kg of material.
• without changing its temperature.

Question 3

What makes up the internal energy of a body?

Answer 3

The sum of:
- The kinetic energy.
- The potential energy.
… of all particles.

• This is randomly distributed.

Question 4

What happens to the internal energy when the state of a substance changes?

Answer 4

• potential energy of the system changes.

- kinetic energy of the system is kept constant.

Question 5

How would you go about answering this question?

“A kettle has power 1200W and contains 0.5kg of water at 22ᵒC, how long will it take for the water in the kettle to reach 100ᵒC? (specific heat capacity of water = 4200 J/kgᵒC)”

Answer 5

• First, find the energy required to increase the temp of water to 100ᵒC using E=mcΔT
• Power = energy transferred over time, so to find the value of time taken you to divide the energy by the power.

Question 6

How would you go about answering this question?

“An ice cube of mass 0.01 kg at a temperature of 0°C is dropped into a glass of water of mass 0.2 kg, at a temperature of 19°C. What is the final temperature of the water once the ice cube has fully melted? (specific heat capacity of water = 4200 J/kg°C, specific latent heat of fusion of ice = 334 J/kg)”

Answer 6

• First, find the energy required to change the state of ice using E = Lm
• Next, you must set up a pair of simultaneous equations to show the energy transfer in the water and in the ice separately:
  
  • for ice:
    E = Lm + mcΔT (as the ice has changed state and temp)
  • for water:
    E = mcΔT
• As we know that the energy transfer is the same in both as the system is closed, we can equate these values to find the final temperature (T).

Question 7

What properties does something that is at absolute 0 have?

Answer 7

• 0K (or -273ᵒC).
• no kinetic energy.
• the volume and pressure of a gas are zero.

Question 8

How can you find the average kinetic energy of a molecule?

Answer 8

3/2kT

k = boltzman constant

Question 9

What assumptions are made in the kinetic theory model?

Answer 9

• No intermolecular forces act on the molecules.
• Duration of collisions is negligible in comparison to time between collisions.
• Random motion of molecules, experiencing a perfectly elastic collision.
• motion follows newtons laws.
• Molecules move in a straight line between collisions.

Question 10

Derive pV = 1⁄3Nmc²

Answer 10

• molecule of mass m travels in an area (cube of lengths l) at a velocity of u.
• when it collides with the wall elastically mu = -mu ∴ mu-(-mu) = 2mu.
• when it collides with another wall it would have travelled a distance of 2l ∴ time between collision t = 2l/u.
• we can use the previous information to find the impulse: F = mv/t = 2mu/(2l/u) = mu²/l
• With impulse we can work out pressure: P = (mu²/l)/l² = mu²/l³ = mu²/V
• consider all particles:
  P = m(u₁²+ u₂² + u₃² +…+ uₙ²) /V.
• (u₁²+ u₂² + u₃² +…+ uₙ²) = N(u²)
• P = Nm(u²)/V.

- consider all directions:
(uˣ)² +(uʸ)² +(uᶻ)² = (u²)
(uˣ)² = (uʸ)² = (uᶻ)²
3(u²) = (c²)
(u²) =1⁄3(c²)

• P = 1⁄3Nm(c²)/V.
• pV = 1⁄3Nm(c²).

Question 11

What are the properties of an ideal gas?

Answer 11

• no interactions other than perfect elastic collisions between gas molecules.
• thus there is no intermolecular forces between molecules.
• thus has no potential energy.
• and so, its internal energy = sum of kinetic energies of all of its particles.

Question 12

What equations links p, V, N, and T for an ideal gas?

Answer 12

pV = NkT

p = pressure.
V = volume.
N = number of moelcues.
k = bolzman constant.
T = temperature.

Question 13

Using the kinetic theory model and the ideal gas equation, derive the equation for the average kinetic energy of a molecule?

Answer 13

• pV = 1⁄3Nmc² and pV = NkT
• 1⁄3Nmv² = NkT
• 1⁄3mv² = kT
• 1.5 x 1⁄3mv² = 1.5kT
• ½mv² = 1.5kT = Eₖ

Question 14

What is a black body radiator?

Answer 14

• a perfect emitter and absorber of all possible wavelengths of radiation.

Question 15

What does Stefan’s law describe?

L = σAT⁴

Answer 15

• that the power output (luminosity (L)) of a black body is directly proportional to its surface area and its (absolute temperature)⁴
• σ = Stefans constant

Question 16

What does Wien’s law describe?

λₘₐₓT = 2.898x10⁻³ mK

Answer 16

• The peak wavelength of emitted radiation (λₘₐₓ) is inversely proportional to the absolute temperature (T).

(mK is metres-Kelvin)

• Therefore as a blackbody gets hotter the frequency increases, so the energy of the wave increases.