calculus related rates

Boyle’s law for the expansion of a gas is PV = k, where P is the pressure (in pounds per unit of area), V is the volume of the gas, and k is a constant.
Find the expression that shows the rate of change of the pressure as related to the rate of change of the volume.
dP/dt= ……………………

Evaluate the rate of change of the pressure at the instant when the gas fills 2〖ft〗^3, the pressure is 3000 lb/〖ft〗^2 , and the gas is expanding at 2〖ft〗^3/min
dP/dt= ……………………………

asked by Bill
  1. PV = k
    V dP/dt + P dV/dt = 0

    dP/dt = -(P/V) dV/dt

    Now just plug in your numbers.

    By the way, this is true only if the temperature remains constant. More generally,

    PV = kT

    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. differential calculus

    ADIABATIC EXPANSION when a certain polyatomic gas undergoes adiabatic expansion,its pressure p and volume V satisfy the equation pV^1.3 =k,where k is constant.Find the relationship between the related rates dp/dt and dV/dt. this
  2. Physics

    According to Boyle's law, the volume V of a gas at a constant temperature varies inversely with the pressure P. When the volume of a certain gas is 125 cubic meters, the pressure is 20 psi (pounds per square inch). If the volume
  3. Gas Law Chemistry

    I need help on these two questions: If a certain gas occupies a volume of 16L when the applied pressure is 8.0atm , find the pressure when the gas occupies a volume of 4.0L . A certain gas is present in a 12.0L cylinder at 4.0atm
  4. Anatomy & Physiology

    How do the gas laws (Daltons, Boyles and Henrys)apply to the respiratory processes? I will be happy to critique your thinking on this. I know Dalton's Law is the law of partial pressures, Boyle's law is the law for a fixed mass of
  5. MATH PLEASE HELP!

    According to Boyle's law, the pressure p of a compressed gas is inversely proportional to the volume, v. If a pressure of 20 pounds per square inch exists when the volume of the gas is 500 cubic inches, what is the pressure when
  6. Chemistry

    Two separate flasks are each filled with a gas at 25.0°C; the valve between them is opened and the gases are allowed to mix. What would be the final pressure in torr after mixing, if initially H2 is in the first flask (Volume =
  7. chemistry

    A sample of an ideal gas at 15.0 atm and 10.0 L is allowed to expand against a constant externam pressure of 2.00 atm at a constant temperature. Calculate the work in KJ for the gas expansion (Boyle's law applies)
  8. chemistry

    A fixed quantity of gas at 27°C exhibits a pressure of 729 torr and occupies a volume of 5.70 L. (a) Use Boyle's law to calculate the volume the gas will occupy if the pressure is increased to 1.75 atm while the temperature is
  9. chemistry

    A fixed quantity of gas at 27°C exhibits a pressure of 729 torr and occupies a volume of 5.70 L. (a) Use Boyle's law to calculate the volume the gas will occupy if the pressure is increased to 1.75 atm while the temperature is
  10. chemistry

    A fixed quantity of gas at 27°C exhibits a pressure of 729 torr and occupies a volume of 5.70 L. (a) Use Boyle's law to calculate the volume the gas will occupy if the pressure is increased to 1.75 atm while the temperature is

More Similar Questions