# Partial Derivative Problem

#### cmajor47

1. The problem statement, all variables and given/known data
According to the ideal gas law, the pressure, temperature, and volume of a gas are related by PV=kT, where k is a constant. Find the rate of change of pressure (pounds per square inch) with respect to temperature when the temperature is 300$$^{o}$$K if the volume is kept fixed at 100 cubic inches.

2. Relevant equations

3. The attempt at a solution
PV=kT
P=V-1kT
P=100-1kT
$$\frac{dP}{dT}$$=100-1k

I don't know how to figure this out. We were given the answer, -.01 psi/$$^{o}$$K but I don't know how to get to this with the k there.

#### Tom Mattson

Staff Emeritus
Gold Member
k is Boltzmann's constant.

#### Redbelly98

Staff Emeritus
Homework Helper
This is weird. You're given information (T=300K) which is not necessary for calculating ∂P/∂T, and not given enough information to figure out what k is.

Moreover, pressure should increase as the gas is heated up. Yet "the answer" is a negative quantity!

Something is definitely not right here.

#### Redbelly98

Staff Emeritus
Homework Helper
k is Boltzmann's constant.
That's what I thought when I first saw the problem. But where is the number of gas molecules in PV=kT? Either that equation was not written correctly, or k really is just "a constant".

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