"Why can't a isothemal process be adiabatic?" This was the question my housemate, that studies geology and geography, asked me while studying for his thermodynamics test. As a chemical engineering student I was suppose to be able to answer him immediately, but it took me some pondering to give him a good answer. Lets consider the isothermal expansion of gas, and lets use the convention used by most thermodynamic textbooks that work (W) done by the system on the environment is said to be negative. Consider the diagram and the formula used for work done by isothermal expansion of an ideal gas and the heat formula. Isothermal expansion Work done by isothermal expansion of an ideal gas Heat formula for expansion of an ideal gas in a closed system And because, for reversible isothemal expansion the following is true: For reversible isothermal expansion thus we can see that Q = -W, and W is not equal to 0 because the volume has changed, that mea...