Conservation of entropy -- adiabatic process

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AlexS
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Hello.I have a question about entropy of a thermodynamic system.
1)If we have let say a gas that is separated by some thermo isolated walls (so no heat goes in or out) does the entropy of that gas conserve? I taught that if S=dQ/dt, because Q=0,then the entropy should be conserved.
2)So,does the entropy of a system that undergoes an adiabatic process conserve?
 
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