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.)
= k/min

The temperature of the gas is increasing 0.6577 kelvin/min

Step-by-step explanation:

We have to find the rate of change of T with respect to time at that instant so we should start by arranging the equation

Now we can derivate T to obtain T'

Now we should solve the derivate of (PV) and (nR) by using the product rule

We know that

P=8atm

V=13L

P'=0.14

V'=-0.16

n=10

R=0.0821

n'=0

R'=0

We substitute into the equation

hello from mrbilldoesmath!

answer:

the domain is the set { -2, 0, 2, 3}

discussion:

the domain is the set of x values in the ordered pairs (x,y). taking the x, or first component, of each ordered pair gives   -2, 0, 2, 3.

you,

mrb