One mole of an non liner triatomic ideal gas is expanded adiabaticlly at 300 K from 16 atm to 1 atm Calculate Work done under the following conditions

Question

One mole of an non liner triatomic ideal gas is expanded adiabaticlly at 300 K from 16 atm to 1 atm Calculate Work done under the following conditions

One mole of an non liner triatomic ideal gas is expanded adiabaticlly at 300 K from 16 atm to 1 atm
Calculate Work done under the following conditions
(i) Expansion is carried out reversibly (ii) Expansion is carreid out irrevesibly

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

`q=0`
`w= DeltaU= C_(V)(T_(2)-T_(1))`
`C_(V.)` " for triatomic non linear gas = 3 R
(i) For rev. proecess.
`P_(1)^(1-gamma)T_(1)^(gamma)= P_(2)^(1-gamma)T_(2)^(gamma)" "gamma=(4)/(3)`
`T_(2)= T_(1)(P_(1)/(P_(2)))^((1-gamma)/(V))=300 (2^(4))^(-(1)/(4))=150K`
`DeltaU =w= 3R (150-300)= - 450 R`
(i) n=1
`-P_(ext)(V_(2)-V_(1)) = C_(V)(T_(2)-T_(1))`
`-P_(ext)((RT_(2))/(P_(2))-(RT_(1))/(P_(1)))- = 3R(T_(2)-T_(1))," "-(R)/(16)(16T_(2)-T_(1))=3R(T_(1)-T_(1))`
`-16T_(2)+T_(1)=48T_(2)- 48T_(1)`
`49T_(1)= 64T_(2)`
`T_(2)= (49)/(64)xx300" "rArr" "T_(2) = 229.69`
`w_(irr) = C_(V)(T_(1)- T_(1)) + 3R(229.69-300) = - 210.93 R`