What is specific heat capacity?
- The amount of energy required to increase the temperature of 1kg of a substance by 1⁰C.
- without changing its state.
What is specific heat capacity?
- The amount of energy required to change the state of 1kg of material.
- without changing its temperature.
What makes up the internal energy of a body?
The sum of:
- The kinetic energy.
- The potential energy.
… of all particles.
- This is randomly distributed.
What happens to the internal energy when the state of a substance changes?
- potential energy of the system changes.
- kinetic energy of the system is kept constant.
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)”
- 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.
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)”
- 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
- for ice:
- 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).
What properties does something that is at absolute 0 have?
- 0K (or -273ᵒC).
- no kinetic energy.
- the volume and pressure of a gas are zero.
How can you find the average kinetic energy of a molecule?
3/2kT
k = boltzman constant
What assumptions are made in the kinetic theory model?
- 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.
Derive pV = 1⁄3Nmc²
- 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).
What are the properties of an ideal gas?
- 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.
What equations links p, V, N, and T for an ideal gas?
pV = NkT
p = pressure. V = volume. N = number of moelcues. k = bolzman constant. T = temperature.
Using the kinetic theory model and the ideal gas equation, derive the equation for the average kinetic energy of a molecule?
- pV = 1⁄3Nmc² and pV = NkT
- 1⁄3Nmv² = NkT
- 1⁄3mv² = kT
- 1.5 x 1⁄3mv² = 1.5kT
- ½mv² = 1.5kT = Eₖ
What is a black body radiator?
- a perfect emitter and absorber of all possible wavelengths of radiation.
What does Stefan’s law describe?
L = σAT⁴
- 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
What does Wien’s law describe?
λₘₐₓT = 2.898x10⁻³ mK
- 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.
