Irreversible isothermal compression

The irreversible compression of the gas proceeds in one step against a constant external pressure of 3.0atm. The work is given by

w = -P_extΔV = 0.060 Latm

The work done on the gas is positive because the gas is compressed; the surroundings do positive work on the gas.

How do we compute the heat added to the gas? Indirectly! We note that the process is isothermal. The total energy of the ideal gas is

ΔE = n c_VΔT

and since the temperature is constant, ΔT=0 and ΔE=0. Using the first law of thermodynamics

ΔE = q + w

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