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Starting at temperature \[300\text{ }K,\]one mole of an ideal diatomic gas \[(\gamma =1.4)\] is first compressed adiabatically from volume \[{{V}_{1}}\] to \[{{V}_{2}}=\frac{{{V}_{1}}}{16}.\]It is then allowed to expand isobarically to volume \[2{{V}_{2}}\]. If all the processes are the quasi-static then the final temperature of the gas (in \[{}^\circ K\]) is (to the nearest integer) _______. [JEE MAIN Held on 09-01-2020 Evening]

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