For adiabatic expansion \({\mathrm{\mathrm{q}=0}}\) For Free expansion, \({\mathrm{\mathrm{P}_{\text {ext }}=0}}\) and \({\mathrm{\mathrm{W}=0}}\) As, \({\rm{W = }} - {{\rm{p}}_{{\rm{ext }}}}.\Delta {\rm{v}}\) \({\mathrm{\mathrm{dU}=\mathrm{q}+\mathrm{w} \quad\left[1^{\text {st }}\right.}}\) law of thermodynamics \({\mathrm{]}}\) \({\mathrm{\mathrm{q}=0, \mathrm{w}=0, \mathrm{dU}=0}}\) \({\mathrm{\mathrm{dU}=\mathrm{nC}_{\mathrm{v}}\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right)}}\) \({\mathrm{0=\mathrm{nC}_{\mathrm{v}}\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right)}}\) \({\mathrm{\mathrm{T}_{1}=\mathrm{T}_{2}}}\) i.e., \({\mathrm{\Delta \mathrm{T}=0}}\) So \({\mathrm{\mathrm{q}=0, \Delta \mathrm{T}=0, \mathrm{w}=0}}\) So, the correct option is (3).
JEE Main - 2024
CHXI06:THERMODYNAMICS
369344
When 1 mole of \(\mathrm{CO}_{2(g)}\) occupying volume \(10 \mathrm{~L}\) at \(27^{\circ} \mathrm{C}\) is expanded under adiabatic condition, temperature falls to \(150 \mathrm{~K}\). Hence, final volume is
For adiabatic expansion \({\mathrm{\mathrm{q}=0}}\) For Free expansion, \({\mathrm{\mathrm{P}_{\text {ext }}=0}}\) and \({\mathrm{\mathrm{W}=0}}\) As, \({\rm{W = }} - {{\rm{p}}_{{\rm{ext }}}}.\Delta {\rm{v}}\) \({\mathrm{\mathrm{dU}=\mathrm{q}+\mathrm{w} \quad\left[1^{\text {st }}\right.}}\) law of thermodynamics \({\mathrm{]}}\) \({\mathrm{\mathrm{q}=0, \mathrm{w}=0, \mathrm{dU}=0}}\) \({\mathrm{\mathrm{dU}=\mathrm{nC}_{\mathrm{v}}\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right)}}\) \({\mathrm{0=\mathrm{nC}_{\mathrm{v}}\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right)}}\) \({\mathrm{\mathrm{T}_{1}=\mathrm{T}_{2}}}\) i.e., \({\mathrm{\Delta \mathrm{T}=0}}\) So \({\mathrm{\mathrm{q}=0, \Delta \mathrm{T}=0, \mathrm{w}=0}}\) So, the correct option is (3).
JEE Main - 2024
CHXI06:THERMODYNAMICS
369344
When 1 mole of \(\mathrm{CO}_{2(g)}\) occupying volume \(10 \mathrm{~L}\) at \(27^{\circ} \mathrm{C}\) is expanded under adiabatic condition, temperature falls to \(150 \mathrm{~K}\). Hence, final volume is
For adiabatic expansion \({\mathrm{\mathrm{q}=0}}\) For Free expansion, \({\mathrm{\mathrm{P}_{\text {ext }}=0}}\) and \({\mathrm{\mathrm{W}=0}}\) As, \({\rm{W = }} - {{\rm{p}}_{{\rm{ext }}}}.\Delta {\rm{v}}\) \({\mathrm{\mathrm{dU}=\mathrm{q}+\mathrm{w} \quad\left[1^{\text {st }}\right.}}\) law of thermodynamics \({\mathrm{]}}\) \({\mathrm{\mathrm{q}=0, \mathrm{w}=0, \mathrm{dU}=0}}\) \({\mathrm{\mathrm{dU}=\mathrm{nC}_{\mathrm{v}}\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right)}}\) \({\mathrm{0=\mathrm{nC}_{\mathrm{v}}\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right)}}\) \({\mathrm{\mathrm{T}_{1}=\mathrm{T}_{2}}}\) i.e., \({\mathrm{\Delta \mathrm{T}=0}}\) So \({\mathrm{\mathrm{q}=0, \Delta \mathrm{T}=0, \mathrm{w}=0}}\) So, the correct option is (3).
JEE Main - 2024
CHXI06:THERMODYNAMICS
369344
When 1 mole of \(\mathrm{CO}_{2(g)}\) occupying volume \(10 \mathrm{~L}\) at \(27^{\circ} \mathrm{C}\) is expanded under adiabatic condition, temperature falls to \(150 \mathrm{~K}\). Hence, final volume is
For adiabatic expansion \({\mathrm{\mathrm{q}=0}}\) For Free expansion, \({\mathrm{\mathrm{P}_{\text {ext }}=0}}\) and \({\mathrm{\mathrm{W}=0}}\) As, \({\rm{W = }} - {{\rm{p}}_{{\rm{ext }}}}.\Delta {\rm{v}}\) \({\mathrm{\mathrm{dU}=\mathrm{q}+\mathrm{w} \quad\left[1^{\text {st }}\right.}}\) law of thermodynamics \({\mathrm{]}}\) \({\mathrm{\mathrm{q}=0, \mathrm{w}=0, \mathrm{dU}=0}}\) \({\mathrm{\mathrm{dU}=\mathrm{nC}_{\mathrm{v}}\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right)}}\) \({\mathrm{0=\mathrm{nC}_{\mathrm{v}}\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right)}}\) \({\mathrm{\mathrm{T}_{1}=\mathrm{T}_{2}}}\) i.e., \({\mathrm{\Delta \mathrm{T}=0}}\) So \({\mathrm{\mathrm{q}=0, \Delta \mathrm{T}=0, \mathrm{w}=0}}\) So, the correct option is (3).
JEE Main - 2024
CHXI06:THERMODYNAMICS
369344
When 1 mole of \(\mathrm{CO}_{2(g)}\) occupying volume \(10 \mathrm{~L}\) at \(27^{\circ} \mathrm{C}\) is expanded under adiabatic condition, temperature falls to \(150 \mathrm{~K}\). Hence, final volume is
