# Thread: Chem with partial Derivs

1. ## Chem with partial Derivs

What's given:
PV=nRT P is pressure, T temperature, V volume, n moles, r is ideal gas constant (.08206)

Assume that we have ten moles of gas in a balloon type bladder. Initially we have a volume of 224.15 liters at Standard Temperature and Pressure. (T=273.15, P=1atm) As time goes on gas is heated. The following equation expresses the temperature T of the gas as a function of time elapsed, t since the beginning of the experiment:
T= 323.15 - (50/(t+1))

The bladder begins to expand over time as a function also of the strength S of its material with the following formula describing how the volume V of the gas which can occupy the bladder changes as a function of the number of minutes and the material strength S

V= 4-2e^(-3ts)

a) Describe, by means of an appropriate partial derivative, how the pressure of the gas in the bladder changes as a function of time.

b) Describe by means of an appropriate partial derivative how the pressure of the gas in the bladder changes as a function of the strength of the bladder.

ok... so I've gotten kind of lost with this problem. My first thoughts were to plug formula V & T, and number N(10 moles) into the PV=nRT formula then derive with respect to T, then do the same with respect to S. Is this on the right track?

2. If $\displaystyle P=nR\frac{323.15-\frac{50}{t+1}}{4-2 e^{-3ts}}$ then what is $\displaystyle \frac{\partial P}{\partial t}$ and $\displaystyle \frac{\partial P}{\partial s}$?