A) \[{{T}_{1}}V\,{{_{1}^{\gamma }}^{-1}}={{T}_{2}}V\,{{_{2}^{\gamma }}^{-1}}\]
B) \[{{P}_{1}}V\,{{_{1}^{\gamma }}^{-1}}={{P}_{2}}V\,{{_{2}^{\gamma }}^{-1}}\]
C) \[{{T}_{1}}P\,_{1}^{\gamma }={{T}_{2}}P\,_{2}^{\gamma }\]
D) \[{{T}_{1}}V\,_{1}^{\gamma }={{T}_{2}}V\,_{2}^{\gamma }\]
Correct Answer: A
Solution :
For adiabatic process \[{{P}_{1}}{{V}_{1}}^{\gamma }={{P}_{2}}{{V}_{2}}^{\gamma }\] \[\frac{R{{T}_{1}}}{{{V}_{1}}}{{V}_{1}}^{\gamma }=\frac{R{{T}_{2}}}{{{V}_{2}}}{{V}_{2}}^{\gamma }\] \[{{T}_{1}}{{V}_{1}}^{\gamma -1}={{T}_{2}}{{V}_{2}}^{\gamma -1}\]
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