Adiabatic compression?

If a gas is adiabatically compressed and the calculated change in internal energy is 1600J, is the WORK done on the gas also 1600J??

Answer:
The answer is yes. Since there is no heat loss from the system, all the work done on the gas goes to increasing the internal energy of the gas. From the 1st law of thermodynamics

dU + δW = δQ = 0 for adiabatic systems, therefore

dU = - δW

In the above equations, U = internal energy, W = work done BY the system, and Q = heat transfer across the system boundaries.

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