Option 1 states that if the work done on the system or by the system is zero, the change in internal energy of the gas is equal to the flow of heat in or out of the system. In other words, when no work is being done on the gas or by the gas, any change in internal energy is solely due to the heat flow.

Option 2 suggests that the change in internal energy is less than the heat transferred. This statement contradicts the first law of thermodynamics, which states that the change in internal energy is equal to the heat transferred minus the work done. Therefore, option 2 is incorrect.

Similarly, option 3 claims that the change in internal energy is more than the heat flow, which also contradicts the first law of thermodynamics. According to the first law, the change in internal energy is equal to the heat transferred minus the work done, not more than the heat flow.

Option 4 states that the answer cannot be determined. However, we can determine the correct answer based on the first law of thermodynamics, which states that in the absence of work done on or by the system, the change in internal energy is equal to the heat flow. Therefore, option 4 is incorrect.

In conclusion, option 1 is