Suppose that subsequent to this heating, 1.40 104 J of thermal energy is removed

Question

Suppose that subsequent to this heating, 1.40 104 J of thermal energy is removed from the gas isothermally. Find the final volume in terms of the initial volume of the example, V0. (Hint: Follow the same steps as in the example, but in reverse. Use the values in the Practice It section. Also note that the initial volume in this exercise is 1.25 V0.)
Vf =

V0
Are you expecting the final volume to be larger or smaller than 1.25V0?

Explanation / Answer

sol For the first part I get the same result W = - n·R·T·ln( V_final/V_initial ) Q = -W = n·R·T·ln( V_final/V_initial ) Q = -W = n·R·T·ln( V_final/V_initial ) Q/(n·R·T) = ln( V_final/V_initial ) => V_final = V_initial · e^( Q/(n·R·T) ) with V_initial = 1.25·V0 Q = - 1.2×104 J (negative because heat is removed) n = 4.40 mol R = 8.3145 Jmol?¹K?¹ T = 301K so we get V_final = 1.25 · V0 · e^(-1.08975) = 0.42·V0

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