Find out the work done to expand an ideal gas isothermally to twice it

1.	Find out the work done to expand an ideal gas isothermally to twice its initial volume.
Answer» Solution :If 1 mol of an ideal gas is at a temperature T K. then `pV = RT or, p = (RT)/(V)` `:.` Work k done is isothermal PROCESS, `W = int_(V_i)^(V_f) pdV = int_(V_i)^(V_f) (RT)/V = dV = RT int_(V_i)^(V_f)(dV)/V = RT In(V_f)/(V_i)` [T = constant in isothermal process] Here, `(V_f)/(V_i) = 2 and R = 8.31 J cdot mol^(-1) cdot K^(-1)` `:. W = 8.31 XX T xx In2 = 8.31 xx 0.693 T` `= 5.76 T J`.

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