Gas law homework question.

Question

The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant. Suppose that, at a certain instant, P = 7.0 atm and is increasing at a rate of 0.13 atm/min and V = 13 L and is decreasing at a rate of 0.17 L/min. Find the rate of change of T with respect to time at that instant if n = 10 mol. (Round your answer to four decimal places.)

Answer 1

T=PV/(nR)

Differentiate with respect to time(t)

dT/dt = (1/nR)[P(dV/dt)+V(dP/dt)

Plug in the values and do the arithmetic.

(7*.17)=1.19

13*.13=1.69

(1.19+1.69)/.821=3.5079....BUT this level of significant digits is NOT justified by the data

P.S.

I just assume that the units given are consistent!