Suppose the pressure P of a gas is a differentiable function of temperature T an

Question

Suppose the pressure P of a gas is a differentiable function of temperature T and volume V. From the list at the bottom, choose the function you would use to determine each of the following measurements or estimates. Choose the one best answer for each question. (There will be one function that you do not use.) (a) Find the exact pressure at a given temperature and volume. (b) Estimate the pressure for temperatures and pressures near a fixed temperature and pres- sure. (c) Estimate how pressure changes if temperature and volume change. (d) Measure the rate of change of pressure as temperature changes and volume is held con stant. (e) Measure the rate of change of pressure in a given direction._

Explanation / Answer

I dont see the list from which we must choose....

a)
To do this ,we will choose the given function P(T,V)

b)
For this, we will first linearize it and then
use the linearized function to find the pressure

c)
For this, we need to find the partial derivatives of P
with V and with T and work with those functions

d)
For this, we use the partial derivative of P with T
as in dP/dT

e)
For this, we will use the directional derivative

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