The speed of sound (in m/s) in dry air is approximated the fun...

Question

The speed of sound (in m/s) in dry air is approximated the function v(T) = 331 + 0.6T, where T is the air temperature (in degrees Celsius). Evaluate v' (T) and interpret its meaning.

Accepted Answer

Hello. In this video, we are going to be solving the following pressure problem. So we are told that the pressure P in kilopascals of a gas in a sealed container is given by the function P of V is equal to 100 minus 0.4V. This is where V is the volume of the gas in liters. We want to determine the derivative PV and explain its significance. So, let's first start by finding the derivative P V. Now, we are given the original function PV, and it is equal to 100 minus 0.4 V. Let's go ahead and take the derivative of PV. So P V, well, how do we find its derivative? First, we take the derivative of the constant value 100, but the derivative of constant value will always be zero. So the derivative of the first term is zero. Now, what about the derivative of negative 0.4 V? Well, by the power rule, that derivative is going to be negative 0.4. And that means that our derivative PV is going to be the constant function negative 0.4. But what does PV tell us? Well, PV represents the rate of change of the pressure with respect to the volume. And since the derivative is a negative constant function, what this tells us is that for every 1 L increase in volume, the pressure is going to decrease by 0.4 kilopascales. So that is the significance of PV. And with that being said, the solution to this problem is going to be a. So, I hope this video helps you in understanding how to approach this problem, and I will go ahead and see you all in the next video.

The speed of sound (in m/s) in dry air is approximated the function v(T) = 331 + 0.6T, where T is the air temperature (in degrees Celsius). Evaluate v' (T) and interpret its meaning.

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