Question

Two samples of helium with the same number of molecules in each sample are brought to different temperatures. The first sample is heated to 50 degrees Celsius and the second is heated to 100 degrees Celsius. What can be said about the two samples of molecules?

Answer 1

The sample of helium at 100 degrees Celsius will have greater average kinetic energy and internal energy compared to the sample at 50 degrees Celsius, but both will be in the same gaseous state since they are above 25°C.

Step-by-step explanation:

Two samples of helium gas with an equal number of molecules are heated to different temperatures: one to 50 degrees Celsius and another to 100 degrees Celsius. According to the kinetic theory of gases, if both samples are at different temperatures, their average kinetic energies will differ as well. The higher the temperature, the greater the average kinetic energy of the gas molecules. Therefore, the sample of helium at 100 degrees Celsius will have a higher average kinetic energy compared to the sample at 50 degrees Celsius. However, since the number of molecules is the same and both samples are at a temperature above 25°C (at which helium is a gas), we can say they are in the same physical state, specifically the gaseous state.

Physical properties such as pressure or volume would also differ between the two samples, assuming they are in containers with the same volume. However, another important point is that, at a given temperature for ideal gases, the internal energy is dependent only on temperature, implying that the internal energy of the sample at 100 degrees Celsius will be higher than that of the sample at 50 degrees Celsius.