Integrated Concepts

Hot air rises because it has expanded. It then displaces a greater volume of cold air, which increases the buoyant force on it. (a) Calculate the ratio of the buoyant force to the weight of $50.0º \text{C}$ air surrounded by $20.0º \text{C}$ air. (b) What energy is needed to cause $1.00 \text{ m}^{3}$ of air to go from $20.0º \text{C}$ to $50.0º \text{C}$? (c) What gravitational potential energy is gained by this volume of air if it rises 1.00 m? Will this cause a significant cooling of the air?