devarshi-dt-logo

Question:

One mole of a monoatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is 100K and the universal gas constant R = 8.0 J/molK, the decrease in its internal energy, in Joule, is ________.

Solution:

vi = v
F = 8v
For an adiabatic process γ = 5/3 for monoatomic process
T1V1γ-1 = T2V2γ-1
100(v)2/3 = T2(8v)2/3
T2 = 25K
ΔU = nCvΔT = 1[(3R/2)][100-25] = 1(3/2 x 8)(75) = 900 Joule