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A househusband is cooking beef stew for his family in a pan that is \((a)\) uncovered, \((b)\) covered with a light lid, and \((c)\) covered with a heavy lid. For which case will the cooking time be the shortest? Why?

Short Answer

Expert verified
The case with the heavy lid (c) results in the shortest cooking time for beef stew. This is because the heavy lid helps retain heat, distribute heat evenly, reduces evaporation, and allows for pressure buildup inside the pan, creating a more efficient and faster cooking process.

Step by step solution

01

Heat Retention

First, we need to consider how much heat is being retained in the pan for each case. For the pan to be heated quickly and efficiently, there must be a sufficient amount of heat retention. The uncovered pan will lose the most heat because there is no barrier to retain the heat inside. Both the light lid and heavy lid will retain heat more effectively, with the heavy lid likely retaining the most heat due to its heavier mass.
02

Heat Distribution

Heat distribution is important for even and efficient cooking. A heavy lid would typically provide better heat distribution as it can absorb and distribute heat more evenly, while a light lid might not distribute the heat as evenly. An uncovered pan may have uneven heat distribution due to heat escaping from the open top.
03

Evaporation

Evaporation plays a crucial role in cooking time. In the uncovered pan, there will be more evaporation, which results in the stew reducing and thickening more quickly. In the cases with the light lid and heavy lid, evaporation is reduced, since the lids help contain the moisture and steam.
04

Pressure Buildup

Pressure buildup can also affect cooking time. In the uncovered and light lid cases, there is little to no pressure buildup inside the pan. Conversely, the heavy lid may create some pressure buildup, as it forms a better seal, preventing steam escape. Increased pressure typically results in faster cooking times.
05

Comparing the Cases

Comparing the heat retention, heat distribution, evaporation, and pressure buildup in the three cases, we can conclude that: - (a) Uncovered pan: Fastest reduction and thickening due to more evaporation, but loses heat more quickly and may have uneven heat distribution. - (b) Light lid: Reduces evaporation and retains heat better than the uncovered pan but may still have uneven heat distribution. - (c) Heavy lid: Reduces evaporation, retains heat more efficiently, has better heat distribution, and can build up pressure for faster cooking.
06

Conclusion

The cooking time will be the shortest for the case \((c)\) covered with a heavy lid. This is because the heavy lid helps retain heat, distribute heat evenly, reduces evaporation, and allows for pressure buildup inside the pan. These factors contribute to a more efficient and faster cooking process, resulting in the shortest cooking time.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Heat Retention
Understanding heat retention is crucial when preparing meals, as it directly influences cooking efficiency and time. This concept refers to the capability of a cookware item to maintain heat within its confines. When a pan is left uncovered, heat easily escapes into the environment, cooling the contents at a faster rate. Covering a pan with a lid, particularly a heavy one, acts as an insulating barrier, leading to increased heat retention. This is because the mass of a heavy lid can absorb and hold onto the heat better than a lighter one, which can result in a quicker cooking process due to less energy loss. Moreover, better heat retention ensures that the temperature within the pan remains steady, producing more consistent cooking outcomes.
Heat Distribution
Heat distribution is another vital element to consider when cooking. It determines how uniformly the heat is spread across the cooking surface. When using an uncovered pan, the heat tends to concentrate at the bottom, often causing uneven cooking and the potential for burning. However, covering the pan with a lid, particularly one that is heavy, can greatly improve the distribution of heat. The lid absorbs heat, which then radiates throughout the surface, leading to even cooking. This avoids hot spots that might occur in an uncovered pan and ensures that the food is uniformly cooked through, which is advantageous, especially for dishes like stews, where consistent temperatures help to tenderize meats and meld flavors.
Evaporation in Cooking
Evaporation is a common phenomenon in cooking, particularly in methods like simmering or boiling. It refers to the process where liquid turns into vapor and escapes into the air, which can significantly affect the cooking time and the concentration of flavors. In an uncovered pan, evaporation occurs at a rapid rate, leading to a reduction in liquid volume and a thicker, more concentrated stew. While this might be beneficial for certain recipes requiring reduction, it also necessitates more frequent monitoring to prevent the dish from drying out. Covering the pan with a lid minimizes evaporation by trapping moisture and steam, which helps maintain a constant volume and prevents the dish from becoming overly thick before the ingredients are properly cooked.
Pressure Buildup in Cooking
The concept of pressure buildup in cooking is prominent in methods like pressure cooking, but it's also relevant when using a lid on a pan. When a heavy lid is placed on a pan, it helps to seal the edges more effectively, limiting the escape of steam and causing a slight increase in the internal pressure. This incremental pressure rise lowers the boiling point of water, thereby speeding up the cooking process. In contrast, using a light lid or leaving the pan uncovered does not create the same level of pressure. As such, a heavy lid can contribute to a faster cooking time by using the principles of increased pressure similar to those in a pressure cooker, although to a lesser extent. This can be especially useful for cooking foods that benefit from a moist, high-heat environment, such as stews and braises.

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Most popular questions from this chapter

Water initially at 200 kPa and \(300^{\circ} \mathrm{C}\) is contained in a piston-cylinder device fitted with stops. The water is allowed to cool at constant pressure until it exists as a saturated vapor and the piston rests on the stops. Then the water continues to cool until the pressure is \(100 \mathrm{kPa}\). On the \(T\) -v diagrams sketch, with respect to the saturation lines, the process curves passing through both the initial, intermediate, and final states of the water. Label the \(T, P\) and \(v\) values for end states on the process curves. Find the overall change in internal energy between the initial and final states per unit mass of water.

Superheated water vapor at 180 psia and \(500^{\circ} \mathrm{F}\) is allowed to cool at constant volume until the temperature drops to \(250^{\circ} \mathrm{F}\). At the final state, determine \((a)\) the pressure, (b) the quality, and ( \(c\) ) the enthalpy. Also, show the process on a \(T\) -v diagram with respect to saturation lines.

A \(1-m^{3}\) tank containing air at \(10^{\circ} \mathrm{C}\) and 350 kPa is connected through a valve to another tank containing \(3 \mathrm{kg}\) of air at \(35^{\circ} \mathrm{C}\) and 200 kPa. Now the valve is opened, and the entire system is allowed to reach thermal equilibrium with the surroundings, which are at \(20^{\circ} \mathrm{C}\). Determine the volume of the second tank and the final equilibrium pressure of air. Answers: \(1.33 \mathrm{m}^{3}, 264 \mathrm{kPa}.\)

Water initially at \(300 \mathrm{kPa}\) and \(0.5 \mathrm{m}^{3} / \mathrm{kg}\) is contained in a piston-cylinder device fitted with stops so that the water supports the weight of the piston and the force of the atmosphere. The water is heated until it reaches the saturated vapor state and the piston rests against the stops. With the piston against the stops, the water is further heated until the pressure is 600 kPa. On the \(P\) -v and \(T\) -v diagrams sketch, with respect to the saturation lines, the process curves passing through both the initial and final states of the water. Label the states on the process as \(1,2,\) and \(3 .\) On both the \(P\) -v and \(T-v\) diagrams, sketch the isotherms passing through the states and show their values, in \(^{\circ} \mathrm{C}\), on the isotherms.

A spherical balloon with a diameter of \(9 \mathrm{m}\) is filled with helium at \(27^{\circ} \mathrm{C}\) and 200 kPa. Determine the mole number and the mass of the helium in the balloon. Answers: \(30.6 \mathrm{kmol}, 123 \mathrm{kg}.\)

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