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Question:

If the door of the refrigerator is kept open, the room in which the refrigerator is kept:

  1. gets cooled
  2. gets heated
  3. neither gets cooled nor gets heated
  4. gets cooled or heated depending on the initial temperature of the room.

The answer mentioned is option b) gets heated It doesn't seem convincing that on opening refrigerator's door the room gets heated. Also the radiator emits out the heat in the surrounding. Thus the heat absorbed from the room is released in it and the must neither get cooled nor heated.

Just before posting this question I have tried to experimentally verify this and observed no change in temperature of the room.

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  • $\begingroup$ I think at first pass this looks like homework but is not. I have edited and believe the question should remain open. $\endgroup$ – A.K. Apr 6 '19 at 1:46
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    $\begingroup$ Not sure if you'd call it duplicate(from a different site), but I mention it anyway: Opening the fridge door to cool a room $\endgroup$ – William R. Ebenezer Apr 6 '19 at 6:18
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Also the radiator emits out the heat in the surrounding. Thus the heat absorbed from the room is released in it and the must neither get cooled nor heated.

You have forgotten a few parts to your system in how a refrigerator pumps heat. You have assumed a spontaneous steady state cycle of:

$$\text{radiator}\underset{\text{conduction}}{\overset{\text{heat pump}}\leftrightharpoons} \text{fridge}$$

But that is not true to move heat from a low-temperature body body to a high-temperature body requires an input of work which is added to the heat dumped into the high-temperature body.

heat pump cycle

In this case work is done by the compressor which takes in electrical energy and transforms it into work and heat. Since electrical energy is 100% efficient at heating any electrical energy consumed by the compressor is eventually converted into heat either by ohmic heat, efficiency losses or work being converted into heat at the high-temperature body. Since your high-temperature body and low-temperature body are allowed to conduct/convect/radiate/transfer heat between the two sinks, heat overall is added to the room.

Just before posting this question I have tried to experimentally verify this and observed no change in temperature of the room.

There are a number of problems with this, and why you may not have observed anything.

  1. Rooms are not closed nor isolated systems thus are subject to many thermal variations from light (radiation), drafts (convection), and conduction of heat through walls to/from the outside which can make your results unreliable.
  2. A the heat capacity of a room is very large and it will take a while for your fridge to impart a change that a thermostat/thermometer can detect.
  3. The energy consumed by a refrigerator is relatively small* and it will again take a while for your fridge to impart a change that a thermostat/thermometer can detect.

All and all, such an experiment would require better control than your average room/kitchen. If you did do such a controlled experiment you would observe that the temperature of the room would rise with time due to the heat losses of the compressor.

*I understand some parents/utility customers (possible yours) may find this statement controversial. Kids do not quote me at home.

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Think of a refrigerator as a device that transfers heat from inside a box to its surroundings. The room around a refrigerator is warmed as it receives the heat removed from inside the box.

If you leave the door open, heat is merely recycled from the room into the refrigerator, then back into the room. A net room temperature increase would result from the heat of the motor that would be constantly running to move energy around in a circle. It would be like hooking up a water pump to remove water from your basement and routing the discharge tube back to the basement.

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Energy balance

No matter if you leave the door open or closed, if you run a refrigerator in a room (system) that is thermally insulated with its surrounding, the energy of the room will increase.

The reason is that your are performing electrical work on the system (the refrigerator is plugged in and is drawing power). According to the first law of thermodynamics, energy is conserved. If you are looking at a closed system (no transfer of matter), the change in energy of the system is equal to the work done on the system and the heat transferred into the system. If you are looking at an isolated system (no transfer of matter or heat), the only change in energy is through work done on or by the system.

Temperature

Whether the temperature goes up or not depends on what else is in the room. If there is nothing else but the refrigerator in the room, and the refrigerator was turned off before, as soon as you turn on the refrigerator the room temperature will increase. If the refrigerator door is closed, the inside of the refrigerator will decrease in temperature, and the increase in temperature of the rest of the room will be even higher (because of the heat transfer from refrigerator to rest of the room).

However, if your room is filled with water with some ice cubes in it (don't try at home, danger of electrocution), the temperature of the room will remain at about 273K. Instead, the increase in energy will be used to melt some of the ice.

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The "cool" in the refrigerator is made by putting the "heat" into the room. However the process isn't 100% energy efficient. The electric motor that drives the pump generates heat. So overall you're putting heat into the room.

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