The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of an ideal gas are related by the equation PV = 8.31T, where P, V, and T are all functions of time (in seconds). At some point in time the temperature is 270 K and increasing at a rate of 0.1 K/s and the pressure is 12 and increasing at a rate of 0.05 kPa/s. Find the rate at which the volume is changing at that time. L/s Round your answer to four decimal places as needed.

When you use a spray can and press the valve at the top, you decrease the pressure of the gas in the can. This decrease of pressure causes the volume of the gas in the can to increase. Because the gas needs more room than is provided in the can, it expands in spray form through the small hole near the valve. In general, if the temperature is constant, the pressure, P, of a gas in a container varies inversely as the volume, V, of the container. The pressure of a gas sample in a container whose volume is 8 cubic inches is 12 pounds per square inch. If the sample expands to a volume of 22 cubic inches, what is the new pressure of the gas?

In a hybrid-engine vehicle, energy from battery (“b" in Amperes) and from 95 octane unleaded gasoline ("g" in liters) are used intermittently to maximize the distance to be travelled (mileage) between fill- ups and charge-ups. If mileage (M) in kilometers is found out to be: M= 90 b+ 100 g - 3 b' - 5 g? - 2 b g find the values of “b" and “g" that will maximize mileage M, find the maximum mileage and prove that this is a maximum.

A certain amount of an indissoluble substance containing 2 kg of salt in its pores is subjected to the action of 30 liters of water. After 5 min, 1 kg of salt dissolves. Within how long will 99% of the initial amount of salt dissolve? The rate of dissolution is proportional to the amount of salt that does not dissolve and to the difference between the concentration at the given instant and the concentration and the concentration of the saturated solution (1 kg for 3 litres). Give the result in minutes. The Answer should be: 10.47