Question

If the door of a refrigerator is kept open then what will be the effect on the temperature of the room? I am looking for a mathematical explanation.

Answer 1

When the door of a refrigerator is kept open, the refrigerator will continuously expel cold air into the room, and this will have an effect on the room's temperature. To provide a mathematical explanation, we can use a simplified model based on the principles of heat transfer.

Let's assume the following variables:

1. T_fr: Temperature inside the refrigerator (cold temperature).
2. T_room: Initial temperature of the room (before the refrigerator door is open).
3. T_room_new: Temperature of the room after the refrigerator door has been open for some time.

Now, we can consider the following factors:

1. Heat transfer rate: The rate at which heat flows from the refrigerator into the room when the door is open.
2. Room volume: The volume of the room that will be affected by the heat transfer.

The heat transfer rate can be described by the formula:

Heat transfer rate (Q) = U * A * (T_fr - T_room)

where:

• U is the overall heat transfer coefficient (a measure of how well heat transfers between the refrigerator and the room).
• A is the surface area of the refrigerator door (the area from which heat is transferred).

Note that U and A are constants for a given refrigerator model.

The change in room temperature can be approximated by the formula:

ΔT_room = (Q * t) / (m * c)

where:

• Q is the heat transfer rate (as calculated above).
• t is the time for which the refrigerator door remains open.
• m is the mass of air in the room.
• c is the specific heat capacity of air.

Now, it's essential to consider the complexities of the real-world situation, such as the room's insulation, ventilation, and the rate of heat dissipation from the room to the surroundings. In reality, the actual temperature increase in the room will depend on various factors and might not follow a linear pattern.

Additionally, the refrigerator's cooling system will continue to run to maintain the temperature inside the refrigerator, so the heat transfer rate may not remain constant over time.

Keep in mind that the primary purpose of a refrigerator is to maintain a cold temperature inside while preventing the surrounding area from heating up. Therefore, leaving the refrigerator door open for an extended period is inefficient and should be avoided to conserve energy and keep the room temperature stable.