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 = 9 atm and is increasing at a rate of 0.13 atm/min and V = 14 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 moles. (Round to 4 decimal places.) dT/dt = ____k/min

Answer 1

T= (PV)/ (nR)

Answer 2

Note: nR is a constant

Answer 3

\[\frac{dT}{dt} = \frac{1}{nR}[ \frac{d}{dt} (PV)]\]

Answer 4

Now, PV is a product, so use product rule.

Answer 5

\[\frac{dT}{dt} = \frac{1}{nR} [ P \frac{dV}{dt} + V \frac{dP}{dt}] \]

Answer 6

Then sub in the numbers

Answer 7

I don't really remember what the SI units for pressure are.

Answer 8

I just googled it and it says it is pascals, so you need to convert atomshperes to pascals. I think.

Answer 9

the units are not important, because they just ask for the numbers only. But thank you, it makes a whole lot more sense and im finishing the problem now

Answer 10

remember, decreasing rates have negative values.

Answer 11

dV/dt should be a negative value when you sub it into the formula.