Questions: Heat and Internal Energy

Question 1

A cup of coffee cools from 80°C to 20°C sitting on a table. Which statement correctly describes this process?

• A. The coffee lost heat, so it now contains less heat than room-temperature coffee
• B. Heat was transferred from the coffee to its surroundings; the coffee's internal energy decreased
• C. The coffee's temperature fell, but its internal energy stayed the same because the atoms didn't disappear
• D. Heat flowed into the coffee from the room, since the room is at lower temperature

Answer: (B)

Heat is not a substance stored in the coffee — it is the transfer of energy from a hotter to a cooler body. When the coffee cools, its internal energy decreases as heat flows to the surroundings. Option A commits the key misconception: objects don't 'contain heat,' they contain internal energy. Option D reverses the direction — heat flows from hot to cold, not from cold to hot.

Question 2

A lit birthday candle burns at 600°C. A warm bathtub holds water at 40°C. Which contains more internal energy?

• A. The candle, because its temperature is much higher
• B. The bathtub, because it contains vastly more matter with thermal energy
• C. They contain the same internal energy, because thermal equilibrium will eventually equalize them
• D. Temperature and internal energy are unrelated, so neither can be compared

Answer: (B)

Internal energy depends on both temperature and the amount of matter. The bathtub contains billions of times more molecules than the candle flame, each carrying kinetic energy. Even at lower temperature, the total internal energy of the water vastly exceeds that of the tiny candle flame. This scenario illustrates why high temperature does not imply high internal energy — a classic misconception noted in the Common Misconceptions section.

Question 3

When ice melts at 0°C, it absorbs energy without any change in temperature because the energy goes into breaking intermolecular bonds rather than increasing molecular speeds.

• T. True
• F. False

Answer: True

This is latent heat of fusion. At 0°C, the ice and water are in equilibrium — added energy goes entirely into the phase transition (breaking the hydrogen bond network of the crystal lattice), not into raising kinetic energy. Since temperature measures average kinetic energy of molecules, and kinetic energy isn't changing here, temperature stays constant while internal potential energy increases. This directly shows that internal energy and temperature are distinct quantities.

Question 4

A body with a higher temperature usually contains more internal energy than a body at a lower temperature.

• T. True
• F. False

Answer: False

Internal energy depends on both temperature and the quantity of matter. A small, very hot object (like a candle flame at 600°C) contains far less internal energy than a massive cooler object (like a lake at 15°C). Temperature measures the average kinetic energy per molecule; internal energy is the total energy summed over all molecules. This distinction is one of the two key misconceptions identified in this topic.

Question 5

Why is it incorrect to say that a hot object 'contains heat'?

Model answer: Heat is not a substance stored inside a body — it is a process: the transfer of energy across a system boundary driven by a temperature difference. What bodies store is internal energy (U), the total microscopic kinetic and potential energy of their particles. 'Heat' only exists in transit, the way 'work' only exists as a transfer process. Once the transfer ends, the energy is stored as internal energy, not as heat. Saying an object 'contains heat' conflates the stored quantity (U) with the mode of transfer (Q), leading to errors in energy accounting — such as the now-abandoned 'caloric' fluid theory of heat.

The practical importance is that the first law of thermodynamics tracks ΔU = Q + W, where Q and W are modes of transfer, not stored quantities. Internal energy U is a state function (depends only on current state); Q and W are path-dependent transfers. Keeping this distinction sharp prevents errors like adding 'heat' and 'work' as if they were stored commodities.