Why is the accuracy of the experiment being performed here not affected by whether the container is covered with a lid or not?
2 kg of ice at low temperature is heated in an open polystyrene container for 50 minutes using an electrical heater and the temperature recorded at regular intervals.
You have mentioned that the accuracy of the experiment would not be affected, but what is the objective of your experiment in the first place. Are you trying to measure the heat required to melt ice, the specific heat of ice, the conductivity of the polystyrene container, or something else.
If you are trying to accomplish any of objectives that I have provided above, I think there will be a change in the result when the container has a lid and when there is no lid on the container.
You need to specify what you are trying to find through the experiment in a more elaborate way so that a correct answer can be provided.
As stated in the answer posted above, objective of the experiment, and perhaps the accuracy of the results required will determine the need for covering the container with a lid. However, if we say that the purpose of the lid is to provide a layer of insulating material to reduce the loss of heat through the top of the container, then it is interesting to note that the ice remaining in the container will float over the heated water, and act as insulating cover over the water underneath. This action will be very similar to the action of sheets of ice that form over lakes in very cold climates, keeping the lake water warm enough for fishes to survive in it.
If the experiment is continued long enough the ice cover will become gradually thinner and disappear completely after some time.