Two moles of an ideal gas undergo a reversible isothermal expansion at 300 ~K , starting from an initial volume of 5 ~L . If the total heat absorbed by the gas during this process is 3.436 ~kJ , what is the final volume of the gas? Given: R = 8.3 ~J K⁻¹ mol⁻¹ and 2 = 0.69 .

Step-by-step solution

For an isothermal process involving an ideal gas, the change in internal energy is zero ( U = 0 ). According to the First Law of Thermodynamics: U = q + w 0 = q + w w = -q Given that the heat absorbed q = +3.436 ~kJ = +3436 ~J , the work done by the gas is: w = -3436 ~J The work done in a reversible isothermal expansion is given by: w = -nRT ( V_f V_i ) Substitute the given values: -3436 = -2 8.3 300 ( V_f 5 ) -3436 = -4980 ( V_f 5 ) ( V_f 5 ) = 3436 4980 0.69 Since 2 = 0.69 , we have: ( V_f 5 ) = 2 V_f 5 = 2 V_f =