In a thermodynamics process, pressure of a fixed mass of a gas is changed in such a manner that the gas releases $20\,J$ of heat and $8\,J$ of work is done on the gas. If the initial internal energy of the gas was $30\,J$. The final internal energy will be...... $J$
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(Give $2^{1.2}=2.3 ; 2^{3.2}=9.2 ; R$ is gas constant)
$(1)$ The final pressure of the gas mixture after compression is in between $9 P _0$ and $10 P _0$
$(2)$ The average kinetic energy of the gas mixture after compression is in between $18 RT _0$ and $19 RT _0$
$(3)$ The work $| W |$ done during the process is $13 RT _0$
$(4)$ Adiabatic constant of the gas mixture is $1.6$