One Clausius inequality based on an apparatus with a single thermal reservoir is reviewed. Some intricate issues regarding the apparatus are brought up and therefore a preferred way to interpret the Kelvin-Planck statement is suggested. Then it is shown that another Clausius inequality can be established from a direct application of the proposition regarding the efficiency of a Carnot cycle. The establishment is based on an apparatus with two reservoirs, and the resultant inequality involves the temperature of external reservoir. Finally, a different apparatus which also has two thermal reservoirs is utilized to compare the cyclic integral of the former inequality with the one of the latter resulting in the proof of the former inequality which involves the temperature at the system boundary. The applications and limitations of these two Clausius inequalities are discussed.