IES ASK YOUR TEACHER PRACTICE ANOTHER Example Video Example () The pressure P (in kilopascals), volume V (in liters), and temperature 7 (in kelvins) of a mole of an ideal gas are related by the equation PV = 8.317. Find the rate at which the pressure is changing when the temperature is 200 K and increasing at a rate of 0.1 K/s and the volume is 100 L and increasing at a rate of 0.3 L/s. Solution dT - = 0.1, V = 100, dv _ If t represents the time elapsed in seconds, then at the given instant, we have 7 = 200, = 0.3. dt dt Since P = 8.31- T V the chain rule gives the following. (Round your final answer to five decimal places.) dP ap dT OP dv dt aT dt av dt 8.31 dT dv V dt dt 8.31 8.31(200) 100 1002 KPA/S. The pressure is decreasing at a rate (in kPA/s), rounded to three decimal places, of about Need Help? Read It