An insulated, constant-volume system containing 1.36 kg of air receives 53 kJ of paddle work. The initial temperature is 27°C. Determine a) the change of internal energy. b) the final temperature. Assume a mean value C. = 0.718 kJ/kgK.

An insulated, constant-volume system containing 1.36 kg of air receives 53 kJ of paddle work. The initial temperature is ${27}^{\circ }C$. Determine a) the change of internal energy. b) the final temperature. Assume a mean value C. = 0.718 kJ/kgK.
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Given Initial temperature
mass$m=1.36$
Work done W =−53 kJ (since it is externally input work)
Let ${T}_{2}$ be the final temperature

From the first law of thermodynamics
dU= dQ− W
It is an insulated system no heat transfer takes placeso
dQ = 0dU =− WdU = 53 kJdU
is the change in internal energy. We know that Change in internal energy is given by dU = mCvdT

a) the final temperature = 81.266 degree celsius
b) Change in internal energy dU = 53 kJ