At standard temperature and pressure (i.e., 273.15 K and 100 kPa) one mole of an ideal gas has a volume of 22.711 L. For the rest of this question, assume that all the calculations are done for one mole of an ideal gas at standard temperature and pressure.

a. If the pressure is increasing at a rate of 0.3 kPa/s, and the temperature is increasing at 0.1 K/s, how fast is the volume changing?

b. If the volume is increasing at a rate of 0.1 L/s, and the temperature is increasing at 0.1 K/s, how fast is the pressure changing?

c. If the volume is decreasing at a rate of 0.1 L/s, and the pressure is decreasing at 0.1 kPa/s, how fast is the temperature changing?

a. First, three warmup questions about logs.
i. If G(v) = ln(v) what is G 0 (v)?
ii. If H(v) = log10(v) what is H 0 (v)?
iii. If K(u, v) = log10 u v

what is ∂K ∂u ?
Consult Chapter 4 to remind yourself how to differentiate the ln and log10 functions.

b. Calculate ∂(pH)
∂B .

c. Calculate ∂(pH)
∂A .

d. If B and A are both functions of time t (i.e., B = B(t) and A = A(t)), calculate d(pH)
dt .

e. What are the level curves of pH (considered as a function of A and B)?