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  • As insulated container is divided into two equal portions. One portion contains an ideal gas at pressure

As insulated container is divided into two equal portions. One portion contains an ideal gas at pressure \mathrm{P} and temperature \mathrm{T}, while the other portion is a perfect vacuum. If a hole is opened between the two portions, The change in internal energy is :
 

Option: 1

Less than zero


 


Option: 2

Equal to zero
 


Option: 3

More than zero
 


Option: 4

All of the above


Answers (1)

best_answer

As the system is thermally insulated,

\mathrm{ \Delta Q=0 }

Further as here the gas is expanding against vacuum (surroundings), the process is called free expansion and for it,

\mathrm{ \left.\Delta W=\int P d V=0 \quad \text { [as for vacuum } \mathrm{P}=0\right] }

So in accordance with first law of thermodynamics, i.e. \mathrm{\Delta Q=\Delta U+\Delta W},we

have \mathrm{ 0=\Delta U+0 \text {, i.e. } \Delta U=0 \text { or } U=\text { constant } }

So in this problem internal energy of the gas remains constant, i.e. \mathrm{ \Delta U=0 }. Now as for an ideal gas

\mathrm{ U=\frac{3}{2} \mu R T, \quad \text { i.e. } U \propto T }

So temperature of the gas will also remain constant, i.e. \mathrm{ \Delta T=0. }

Posted by

Irshad Anwar

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