# calculus related rates

posted by Bill

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= ……………………………

1. Steve

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

## Similar Questions

1. ### Anatomy & Physiology

How do the gas laws (Daltons, Boyles and Henrys)apply to the respiratory processes?

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 the …
3. ### calculus

Boyle's law states that if the temperature of a gas remains constant, then PV = c. Where P is the pressure, V is the volume, and c is a constant. Given a quantity of gas at constant temperature, if V is decreasing at a rate of 13 in.^3/s, …
4. ### chemistry

A sample of an ideal gas at 15.0 atm and 10.0 L is allowed to expand against a constant external pressure of 2.00 atm at a constant temperature. Calculate the work in units of kJ for the gas expansion. (Hint: Boyle's law applies) Please …
5. ### 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)
6. ### 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 of …
7. ### 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 pressure. …
8. ### Calculus 2

The pressure P of a gas is related to its volume V by the formula P=k/V where k is a constant. A quantity of gas with an initial volume of 1 cubic meter and a pressure of 2.5 newtons per square meter expands to a volume of 16 cubic …
9. ### 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 is …
10. ### algebra

According to Boyle’s law, the volume V of a gas varies inversely to the pressure P exerted by the gas. The volume of a given gas under a pressure of 32 kg per cm2 is 200 cm3. What will be the volume of this gas when the pressure …

More Similar Questions