Need help with A Level physics question about internal energy

So part b) of the question says "A sealed plastic bottle contains 0.05 mole of helium at 20 degrees Celsius. The volume of the gas is 6x10^-4 m^3. Relative molecular mass of helium = 4.0"

Then later on part c) says "The bottle of part b) is now immersed in a water bath of temperature 100 degrees Celsius. Calculate the increase in internal energy of the gas as a result of the immersion of the bottle in the water bath"

According to the mark scheme, the answer to part c) is 50J, but I don't understand why that is? It doesn't show any working out, can anyone explain to me how you'd figure it out please?

Reply 1

Ldk458

I managed to get 50J by doing this:
If you consider a single molecule, the kinetic energy is 3/2 kT (this is in the aqa formula booklet so Im not sure if you have this formula available to use) where k is boltzmann constant and t is temperature in kelvin. Since the substance is a gas, all internal energy is converted to kinetic energy. First work out the change in energy of an individual particle, 3/2k(373) - 3/2k(293) = 1.656 x 10^-21. Then you need to multiply this by the number of molecules present in the container which is 0.05 x avogadros constant = 3.01 x 10^22. Then multiply the change in energy of 1 particle by the number of particles (3.01x10^22 x 1.656x10^-21) to give 49.8 J (3 sf). Hope that helps :smile: