According to basic thermodynamics, heat energy flows spontaneously from one body to another as a result of a difference in which physical quantity?

Introduction / Context:
Understanding why and how heat flows is a central part of thermodynamics. Everyday experience shows that a hot object placed in contact with a cold object cools down while the colder object warms up. This behaviour can be explained using the concept of temperature and thermal equilibrium. This question asks you to identify the physical quantity difference that drives spontaneous heat flow.

Given Data / Assumptions:

• We consider two bodies or regions that may exchange heat.
• Heat transfer is spontaneous, meaning no external work is done to force it.
• Options include temperature, density, mass and volume differences.
• We assume classical thermodynamics with well defined temperatures.

Concept / Approach:
The zeroth law and second law of thermodynamics state that heat flows spontaneously from a body at higher temperature to a body at lower temperature until thermal equilibrium is reached. Temperature is the measure of the average kinetic energy of the microscopic particles in a system. Density, mass and volume may influence how much heat is transferred or the rate of transfer, but they do not in themselves determine the direction of spontaneous heat flow. It is the temperature difference that drives the process of heat transfer by conduction, convection or radiation.

Step-by-Step Solution:
Step 1: Consider two bodies in contact, one hotter and one colder. Step 2: Observationally, the hot body cools while the cold body warms until both reach the same temperature. Step 3: This process is described as heat flowing from the region of higher temperature to the region of lower temperature. Step 4: Even if the masses or volumes of the bodies differ, the direction of spontaneous heat flow depends on which one has higher temperature, not on mass or volume alone. Step 5: Density differences can be important for convection patterns but do not directly set the direction of heat flow; temperature difference does. Step 6: When temperatures become equal, heat flow stops and the system reaches thermal equilibrium. Step 7: Therefore, heat flows as a result of a difference of temperature.

Verification / Alternative check:
Thermodynamic statements such as heat cannot of itself flow from a colder body to a hotter body summarise the second law of thermodynamics. This clearly indicates that the sign of the temperature difference determines the direction of spontaneous heat flow. Mathematical descriptions of conduction, such as Fourier law q proportional to minus k * dT/dx, also show that heat flux is proportional to temperature gradient. Density, mass and volume appear in heat capacity and rate calculations but not as the primary driving difference. All these formulations confirm that temperature difference is the key factor.

Why Other Options Are Wrong:
Density differences influence buoyancy driven convection but do not directly determine the direction of heat flow without an associated temperature difference. Mass determines how much heat a body can store for a given temperature change but does not cause heat to flow on its own. Volume is related to size but, like mass, does not by itself drive heat flow; there must be a temperature difference.

Common Pitfalls:
Students sometimes think that larger or denser objects always lose heat to smaller ones, but this is not true. A small very hot object can transfer heat to a large slightly cooler object because the direction of flow is defined by temperature difference, not by size. It is also easy to confuse temperature with heat; temperature is a measure of thermal state, while heat is energy in transit. Remember that spontaneous heat transfer always occurs down the temperature gradient from higher to lower temperature.

Final Answer:
Heat flows spontaneously because of a difference of Temperature between bodies or regions.