cylinder dealing with related rates

[dear2009]

Dear mathhelp participants,


The ideal gas law states that

PV = nRT,

where P is pressure (in atmospheres), V is volume (in liters), n is the number of moles of gas atoms (a mole contains 6.02 x 1023 atoms), R is the gas constant (0.08206 L atm mol­–1 ­K­–1). Suppose 5 moles of helium is contained in a cylinder whose volume is decreasing at the rate of 2 L/sec, while the pressure is increasing at the rate of ½ atmosphere per second. How fast is the temperature changing when the pressure is 4 atm, the volume is 100 liters, and the temperature is 300K?

All I know is that n is constant

I got 102.36 as my answer


Thanks in advance

 

[arthur ohlsten]

PV=[nR]T
nR are constants, the other terms variables
take derivative with respect to t[time]
P dV/dt + V dP/dt=[nR] dT/dt
dT/dt=-[P dV/dt+ V dP/dt]/nR

dV/dt=-2L/sec
dP/dt=1/2
P=4
V=100
T=300
n=5
R=.08206

Substitute values for numerical answer

Arthur