According to the ideal gas law PV=kT, where P is pressure, V is volume, T is temperature, and k is a constant. Suppose a tank contains 3500 in³of a particular gas at pressure of 24 lb/in.when the temperature is 270 K(degreesKelvin).

a) Determine the constant of proportionality k for this gas.

b) Express the temperature T as a function of P and V using the constant found in part (a) and describe the isotherms for the temperature function.

At a certain factory, the amount of air pollution generated each day is modeled by the function Q=( E, T) 127E^2/3T^1/2where E is the number of employees and T (^oC) is the average temperature during the workday. Currently there are 142 employees and the average temperature is 18^oC. If the average daily temperature is falling at the rate of 0.23^oC/ day and the number of employees is increasing at 3/ month, what is the coressponding effect on the rate of pollution? Express your answer in units/day. For this model, assume there are 22 workdays/ month.