# Students’ Difficulties

I describe the findings with respect to students’ alternative conceptions in the following four topics: 1. Heat and temperature, 2. Thermal equilibrium, 3. First law of thermodynamics 4. Heat transfer mechanisms.

1. Heat and temperature

When asked to explain, what heat is, many students did not go beyond the statement “Heat is a form of energy”. Majority of students could not differentiate between “heat” and “temperature” and they used these terms interchangeably. Some students referred to heat as the “energy content of the system”. They seemed to equate heat with internal energy. For some students, “Heat always increases temperature”, and none showed awareness about the fact that heat might also lead to external work. Some students stated that temperature measures the ‘heat content’ of the body. I found that some students equated temperature to its unit “degree Celsius” whereas some others used inverted reasoning like “temperature causes change in heat”.
The analysis confirmed that thermal equilibrium is an area where students had conceptual difficulties. Students seemed to consider temperature to be an extensive quantity proportional to volume.

2. Thermal Equilibrium:

I probed students’ understanding with respect to

• Understanding thermodynamic variables and thermodynamic equilibrium,
• Confusion between adiabatic and diathermic walls,
• Object size and thermal equilibrium,
• Material of the object and thermal equilibrium,
• Effective temperature of the mixture.

• Understanding thermodynamic variables and thermodynamic equilibrium
• Students were given a situation in which a cylinder (with a gas enclosed in it) fitted with a movable piston was kept on a moving platform. They were asked to identify a thermodynamic variable. About half of them regarded the velocity of any gas molecule to be a thermodynamic variable. They ignored that the velocity of all the molecules has a common component, which is the velocity of the platform as a whole. In elementary kinetic theory, students learn that the average velocity (in magnitude) of a molecule is related to the temperature of the system, which is a thermodynamic variable. Hence they seemed to think that the velocity of a gas molecule is a thermodynamic variable. They ignored the distinction between the velocity of an individual molecule and average velocity per molecule. Another question asked the students explicitly what a thermodynamic variable meant to them. It was rather surprising to note that some students said that any microscopic quantity describing the system is a thermodynamic variable. The correct answer that thermodynamics variable is a macroscopic quantity having a bearing on the internal state of the system, was given only by few students which might have even come through as a random choice. From the responses to another question, it seemed that for some students, equilibrium is “no change in time”. So, they felt that in equilibrium not only the macroscopic but also microscopic variables do not change in time.

• Confusion between adiabatic and diathermic walls
• In one of the questions, the students were asked to categorize materials according to their suitability for adiabatic or diathermic wall. The materials given were plastic, glass, brass, paper, rubber, concrete, diamond, aluminum, gold and Teflon. Out of these, brass, diamond, aluminum, are suitable as diathermic and the others are suitable as adiabatic. This categorization activity brought to my notice the confusion that students had. Students relied heavily on their daily experiences while categorising the materials (For example, “in summer, concrete roof becomes hot… (which) makes us feel hot…” or another example is “… coffee feels hot through glass…”.).
In both these examples, students should have considered the thermal conductivities of concrete and paper, which are very low. It is necessary to understand that for an adiabatic wall these low thermal conductivity materials will take longer time to pass heat through it as compared to diathermic materials like aluminum or brass. Having this practical sense of adiabaticity was absent in students’ understanding.

• Object size and thermal equilibrium
• Students were given a situation in which two wooden cubes of different sizes (27 cm3 and 125 cm3 both initially at room temperature), were kept in a hot air constant temperature enclosure (maintained at 70°C) for a few hours. They were asked to comment on the temperature attained by each cube. A good percentage of them agreed that both the cubes attain a steady temperature but they feltthat the temperature attained by each cube would be different. A sizeable number ofstudents felt that the smaller cube will attain a higher temperature than the bigger cube.

• Material of the object and thermal equilibrium
• Students were given a situation similar to that given above with two cubes of equal sizes but different materials (copper and wood). The cubes were initially at room temperature and then transferred to a hotenclosure at 70°C and kept there for a sufficiently long time. Majority of students replied that the temperature attained by the copper cube would be greater than the temperature attained by the wooden cube as the thermal conductivity of copper is greater than that of wood. Only a small minority opted for the correct option that both the cubes will attainthe same temperature as that of the enclosure. Students seemed to feel that since the rateof increase of temperature of copper will be higher than that of wood, the temperatureattained by it will also be higher.

• Effective temperature of the mixture
• For a question, on the final temperature of mixture of two identical samples of liquid initially at different temperatures (34°C and 96°C), a very small number of students gave the correct answer (65°C). Almost an equal number of students gave the difference of two initial temperatures (62°C) as the answer.

3. First Law of Thermodynamics:

I decided to limit to the cases of adiabatic compression (Q= 0) and isothermal (dU= 0) compression processes leading to simple situation where only two energy terms become non-zero. Further both the adiabatic and isothermal processes are important processes by themselves in elementary thermodynamics. The students’ responses were categorized separately for: temperature,heat, internal energy and sign convention. Students’ written explanations for the selectionof their choice to the items, supported by semi-structured interviews, are presented below.

a. Heat and Temperature:

Students said that since in an adiabatic process, there is no transfer of heat, there should be no temperature change. Similarly, since the word isothermal means that the temperature remainsconstant, for many students there was no heat transfer either. They seemed to know that heat and temperature are not identical but intuitively took them to be inseparable. Among the arguments provided by the students, those based on the ideal gas equation were found to be quite common. The students interpreted the ideal gas equation to mean that the increase in pressure due to compression, whether isothermal or adiabatic, would always be accompanied by an increase in temperature.

b. Internal Energy:

Students stated that in isothermal compression, as the work was doneon the system, the ‘heat content’ of the system increased. They seemed to consider ‘heat content’ equivalent to internal energy. Some students said that since there was no heat transfer in adiabatic compression, the change in the internal energy would be zero. I found that, for some students, in adiabatic compression, the internal energy of the system decreased. For them, there was some kind of ‘natural’ dissipation of internal energy over time and since there was no heat transfer, the internal energy did not get replenished. In the case of isothermal compression, many students predicted that the internal energy of the system would decrease. Perhaps they thought that since the system was open to heat transfer, as the piston moved ‘heat was driven out of the system. Students seemed to be unaware about the fact that the change in the internal energy can be brought about by processes not only due to heating but also by the external work done on the system. Many students showed lack of awareness about how internal energy and temperature were related. Nowhere they used the argument that the gas in the container has been stated to be ideal and that for an ideal gas, the internal energy is dependent only on the temperature. Thus I thought that students’ confusion about heat-internal energy equivalence affected their perception of work done as energy transfer mechanism.

c. Sign Convention:

The students seemed to be unsure of where to apply positive ornegative sign to the work and heat terms in the first law of thermodynamics.

4. Heat Transfer Mechanism:

Students’ prototypical explanations in each case (conduction, convection and radiation) are described below:

1.Conduction:

Students considered heat as a fluid.

A typical response from one student:“. . . the hotness of the heated rod of the metal “expands” as there is space for expansionon the other side of the rod. ..”

2. Convection:

In natural convection, students attributed hotness to single molecules.

A typical response from one student: “. . . cooler water molecules are heated by the warmerwater molecules…”

The hot air blower is an example of forced convection. Most students did not realize this fact and reported this phenomenon as conduction. Since the hot air cannot be seen by the eyes and the hands at a distance are dried by the hot air blower, some students relate this phenomenon to radiation emanating from the blower.