THERMODYNAMICS EXTRA LONG ANSWER RECALL

Explain why a weather balloon expands as it rises through the atmosphere

• At higher altitude, external air pressure decreases

• Balloon contains a fixed mass of gas at a constant temp approx

• From the ideal gas law, pV = Nkt, if p decreases and T is constant, V must increase

• Molecules inside continue colliding with the balloon’s walls.

• Fewer external collisions oppose the expansion

• Therefore the balloon expands until the pressures balance

Explain why food cooks faster in a pressure cooker compared with an open pan

The pressure inside the cooker is greater than atmospheric pressure

From the pressure law, at constant volume, pressure is proportional to absolute temp

Steam and liquid water can reach a higher temperature

Heat transfer to the food is faster as it is in contact with hotter liquid/ steam

So food cooks more quickly

Explain, in terms of kinetic theory, why increasing the temp of a gas does not mean all molecules move at the same higher speed

Temperature is proportional to the mean KE of molecules, not to each molecules speed

The speeds of molecules are spread over a range

As temp increases, the distribution shifts to higher speeds

some molecules will still have relatively low speeds

the most probable speed and r.m.s speed both increase

But molecules do not all move at the same speed

Two stars have the same radius, but one has twice the surface temperature of the other. Compare their luminosities and their colour.

1. From Stefan Boltzmann law, L prop T⁴

2. If one star has double the temperature, its luminosity is 2⁴ = 16 times greater

3. From Wien’s Law, the hotter the star has a shorter peak wavelength

4. Therefore it emits more strongly at the blue end of the spectrum

5. The cooler star is redder and less luminous

6. The hotter star is brighter and appears bluer to an observer