How to solve a multivariable e.g. z=f(x,y), rate of change problem?

The pressure P (in kilopascals), volume V (in liters) and temperature T (in K) of a mole of an ideal gas are related by the equation PV=8.31T. Find the rate at which the pressure is changing when the temperature is 300 K and increasing at a rate of 0.1 K/s and the volume is 100 L and increasing at a rate of 0.2 L/s.

Question

How to solve a multivariable e.g. z=f(x,y), rate of change problem? 

The pressure P (in kilopascals), volume V (in liters) and temperature T (in K) of a mole of an ideal gas are related by the equation PV=8.31T. Find the rate at which the pressure is changing when the temperature is 300 K and increasing at a rate of 0.1 K/s and the volume is 100 L and increasing at a rate of 0.2 L/s.

amistre64 · Answer

im thinking its an implicit wrt.time

amistre64 · Answer

PV=8.31T

P'V+PV' = 8.31T'

P' = (8.31T' - PV') / V

amistre64 · Answer

T = 300  T' = .1

V = 100  V' = .2

P is definable by the stated equation

anonymous · Answer

ok, i try to solve first n let u check the ans k?

amistre64 · Answer

k

anonymous · Answer

correct?? @amistre64

amistre64 · Answer

you might want to include the dimensions to be safe. but yes, as long as the calculations are good, that setup looks fine to me

anonymous · Answer

thx ^_^