Question

What is the driving force for \((a)\) heat transfer, \((b)\) electric current flow, and \((c)\) fluid flow?

Short answer

Answer: The driving forces for these processes are as follows: (a) The driving force for heat transfer is the temperature difference between two points or locations. (b) The driving force for electric current flow is the electric potential difference, also known as voltage, between two points in an electrical circuit. (c) The driving force for fluid flow is often the pressure difference between two points in a fluid system. Other factors such as gravity, viscosity, and external forces can also influence fluid flow.

Step-by-step solution

(a) Driving force for heat transfer

The driving force for heat transfer is the temperature difference between two points or locations. Heat always flows from a high temperature region to a lower temperature region until a thermal equilibrium is reached. The greater the temperature difference, the faster the rate of heat transfer. In mathematical terms, this can be represented using Fourier's law: $$q = -k \frac{dT}{dx},$$ where \(q\) is the heat transfer rate, \(k\) is the thermal conductivity of the material, and \(\frac{dT}{dx}\) represents the temperature gradient.

(b) Driving force for electric current flow

The driving force for electric current flow is the electric potential difference, also known as voltage, between two points in an electrical circuit. The movement of electric charge (current) occurs due to the presence of this potential difference. The greater the voltage difference, the greater the driving force for the current flow. Ohm's law mathematically relates voltage, current, and resistance in a circuit: $$V = IR,$$ where \(V\) is the voltage, \(I\) is the electric current, and \(R\) is the electrical resistance.

(c) Driving force for fluid flow

The driving force for fluid flow is often the pressure difference between two points in a fluid system. Fluid flows from a region of high pressure to a region of low pressure. The greater the pressure difference, the stronger the driving force for fluid flow. In fluid dynamics, this concept is mathematically represented by the Bernoulli equation for ideal, incompressible fluids: $$\frac{1}{2} \rho V^2 + p = \text{constant},$$ where \(\rho\) is the fluid density, \(V\) is the fluid velocity, and \(p\) is the fluid pressure. Other factors such as gravity, viscosity, and external forces can also influence fluid flow.