One mole of a monatomic 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 $$R=8.0J$$ mol−$$1K$$−$$1$$, the decrease in its internal energy, in joule, is .

Question

One mole of a monatomic 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  $$R=8.0J$$ mol−$$1K$$−$$1$$, the decrease in its internal energy, in  joule, is  .

Infinity Learn · Accepted Answer

$$Vi=V$$  $$VF=8V$$  For adiabatic process $${$$γ$$=53$$  for monoatomic $$process}T1V1$$γ−$$1=T2$$.$$V2$$γ−$$1$$⇒$$100V23=T28V23$$⇒$$T2=25KThus$$,   Decrease in Δ$$U=nCv$$Δ$$T=13R2100$$−$$25=12$$×$$75=900J$$

Thermodynamic processes

Remember concepts with our Masterclasses.

One mole of a monatomic 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 $R = 8.0 J m o l^{- 1} K^{- 1}$ , the decrease in its internal energy, in joule, is .

Ready to Test Your Skills?

free study material

Thermodynamic processes

Remember concepts with our Masterclasses.

One mole of a monatomic 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=8.0J mol−1K−1, the decrease in its internal energy, in joule, is .

Vi=V VF=8V For adiabatic process {γ=53 for monoatomic process}T1V1γ−1=T2.V2γ−1⇒100V23=T28V23⇒T2=25KThus, Decrease in ΔU=nCvΔT=13R2100−25=12×75=900J

Ready to Test Your Skills?

free study material

One mole of a monatomic 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 $R = 8.0 J m o l^{- 1} K^{- 1}$ , the decrease in its internal energy, in joule, is .