Answer:
160/13 ≈ 12.3 units per second
Explanation:
The product of pressure and volume is proportional to temperature, and temperature is 100 when pressure and volume are 10 and 13, respectively. You want to know the rate of change of temperature when volume decreases at 1 per second and pressure increases at 2 per second.
Relation
The given proportion can be written with constant of proportionality k as ...
PV = kT
The value of k is ...
k = PV/T = (10)(13)/100 = 1.3
Solving the relation for T, we have ...
T = PV/k = PV/1.3
Rate of change
The rate of change is found by differentiating this product:
T' = (P'V +PV')/k
T' = ((+2)(13) +(10)(-1))/1.3 = (26-10)/1.3 = 16/1.3
T' = 160/13 ≈ 12.3
Temperature is increasing at about 12.3 units per second.