We measured adsorption and desorption isotherms of methane on [Cu(4, 4'-bipyridine)2(BF4)2] (LPC) at 258, 273, and 303 K. Adsorption proceeds almost vertically at a definite pressure, which is named gate pressure. The lower the measurement temperature, the smaller the gate pressure. The temperature dependence of the gate pressure is expressed by the Clapeyron-Clausius equation, giving a thermodynamic evidence on the clathrate formation between the Cu complex and methane.