# Thermodynamics first law

one mole of monatomic gas (in a perfectly insulated cylinder)
has temp = 27 degees c = 300K
volume = 0.025m^3

(gas held in frictionless piston)
heat suppied causes gas to expand at constant pressure gas expands to volume = 0.06m^3

i) calc final temp..
i used pV/T =pV/T (p cancels because its constant) and i got a value for new tempreture as 720K

ii) increase in av. KE per molecule...
using KE= 3/2kT i found the original KE per molecule as 1.49*10^-20
and new KE per molecule as 6.21*10^-21
and the difference between them (increase in av. KE = 8.69*10^-21)

iii) WD by the gas expanding...
WD = p*(change in)V....i got the p value from P = nRT/V and i got that as 99720 Nm-^2 and then multuply by (0.06 -0.025) to get WD as 3490.2 J

iiii) the heat supplied...
i used Q = (change in)u + (change in)WD
change in internal energy (u) is the sum of the change in KE of the molecules right?
so i multiplied change in av. KE per molecule 8.69*10^-21 by avagadros constant to give me KE for one mole, i get a value of 7284.2J

but then i thought that should be the same as...
calculating the change in av. KE of one mole so i used the formula KE = 3/2RT
to find change in KE for a mole and i get a value of 8974.8 - 3739.5 = 5235.3J

shouldnt they be the same, i dont know which ones wrong

anyway i used U as 7284.2J added (WD) 3490.2 to give me Q = 10774.4J

the other one would be Q = 5235.3 + 3490.2 =8725.5J
which ones right?! did i make any mistakes in the other questions?

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