An insulated constant$-$volume system containing $1\mathrm{.}36$ kg of air receives $53$ kJ of particle

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work. The initial temperature is $27C.$ Determine:

$($i$)$ The change in internal energy

$($ii$)$ The final temperature

Assume a mean value $C_v=0\mathrm{.}918k\frac{J}{k}gK$