Are the dimensions of the constant in Newton's Law of Cooling a rate per unit time?

Question

The temperatures cancel out and leave you with 1/time. So I'm assuming the dimensions of the constant would be some value per unit time. Unless its dimensionless?

Thanks!

Answer 1

The left side of the equation is rate of change of the temperature of an object with time; for example, 2 degrees per second.

The right side of the equation is the product of a constant and a temperature difference. If you double the temperature difference between the object and its environment, you will double the rate of change of temperature of the object.

The constant is a measure of heat flow, so it makes sense that its units are in inverse time. A whole lot of physics would go into calculating the value of that constant in a particular situation. That's not the point of the equation. The equation says that, no matter how you calculate the ratio, the rate at which an object's temperature changes is proportional to its temperature difference with respect to its environment.