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 = 8.0 atm and is increasing at a rate of 0.14 atm/min and v = 13 l and is decreasing at a rate of 0.16 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.)dt/dt = k/min

Step-by-step explanation:

We have to calculate the time derivative of T=PV/nR with P and V variable and n and R constants. This is:

What we have to do is the derivative of a product:

Substituting, we have:

where all these values are given since the time derivatives of P and V are their variation rate, using minutes.

We then substitute everything, noticing that already everything is in the same system of units so they cancel out:

And then just calculate:

1 + (6 / x - 1)

step-by-step explanation:

divide using polynomial division.