平静是心情，描述平和的心态 冷静是处世态度，比如冷静处理

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平静can be used to discribe a person or environment, it means very quiet and calm, 冷静 is used to emphasize a PERSON who is very calm when he's in a special (especially a difficult )situation, for exmaple, 飞机失控了，但是机长却很冷静。The captain is very calm even though the aircraft is out of control.