A person cooks a meal in a 30 -cm-diameter pot that is...

A person cooks a meal in a 30 -cm-diameter pot that is covered with a well-fitting lid and lets the food cool to the room temperature of $20^{\circ} \mathrm{C}$. The total mass of the food and the pot is $8 \mathrm{~kg}$. Now the person tries to open the pan by lifting the lid up. Assuming no air has leaked into the pan during cooling, determine if the lid will open or if the pan will move up together with the lid.

Key Concepts

Atmospheric Pressure

Atmospheric pressure is the pressure exerted by the weight of the Earth's air. When the internal pressure of a sealed container drops due to cooling, the higher external atmospheric pressure can act to keep the lid in place, as it pushes down on the lid more than the reduced internal pressure pushes upward.

Force Balance

Force balance is the consideration of all forces acting on an object to determine its state of equilibrium or motion. In this context, it involves comparing the force due to the pressure differential across the lid with the mechanical forces (like the weight of the pot and lid) to decide whether the lid remains sealed or is lifted.

Pressure Differential

A pressure differential is the difference in pressure between two regions. Here, the cooling of the gas in the sealed pot results in a lower internal pressure compared to the atmospheric pressure outside, generating a net force that can affect the movement of the lid.

Ideal Gas Law

The ideal gas law relates pressure, volume, and temperature in a gas. It allows us to understand how cooling in a sealed container leads to a decrease in internal pressure because a reduction in temperature, with volume held constant, causes a corresponding drop in pressure.

Thermal Contraction

Thermal contraction refers to the tendency of the gas inside a container to decrease in pressure or volume as its temperature is lowered. In a sealed situation, cooling causes the contained air to contract, creating a lower internal pressure compared to the external environment.

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