) The Ideal Gas Law is written as PV=mRT, where m is the constant amount of gas (measured in moles), R is the universal gas constant, P is the pressure (function of time), V is the volume (function of time), and T is the temperature (function of time). P,V, and T are all functions of time. This "Law" is only a first order approximation, one which unfortunately, is often not accurate. Frequently, a more correct expression is called a virial expansion of the Ideal Gas Law. The second order virial expansion is given as a second order power series expansion of the pressure term, P=RT(rho+Brho 2
), where rho= V
m
is called the density and B is a function of temperature T (Note that if B is very small then this reduces to the normal Ideal Gas Law). Substitution of rho into (1) yields P= V
mRT
(1+ V
mB
) Suppose that we are studying a gas that obeys this more accurate gas law. Furthermore, suppose that at a certain instant of time, the gas is being cooled at a rate of 3 Cin
C
, the volume is increasing at a rate of 2
1
min
im 3
, the temperature is 4 ∘
C, the volume is 2in 3
,B is 1 m 3
in 3
, and dT
dA
= 4
1
(c)mad in 2
. Use the multivariate chain rule to find the rate at which the pressure is changing with respect to time. In order to receive full credit for this problem you must first draw out the correct chain of dependence and then use this to calculate the derivative dt
dP
. (Notes You must use the multivariate chain rule and a chain of dependence to get full credit for this problem.)