## Boyle’s Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV =

Question

Boyle’s Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant the volume is 900 cm3, the pressure is 100 kPa, and the pressure is increasing at a rate of 40 kPa/min. At what rate is the volume decreasing at this instant?

in progress 0
2 hours 2021-09-15T20:17:40+00:00 1 Answer 0

## Answers ( )

The value of rate of decrease of volume = – 3600

Step-by-step explanation:

According to Boyle’s law P V = C ——- (1)

Pressure ( P ) = 100 k pa = 10

Volume ( V ) = 900

Put these values in equation ( 1 ) we get,

⇒ C = 10 × 900 = 9000 N-cm = 90 N-m

Differentiate Equation ( 1 ) with respect to time we get,

⇒ V + P = 0

⇒ V = – P

= – ———- (2)

This equation gives the rate of decrease of volume.

Given that Rate of increase of pressure = = 40

C = 90 N-m

P =   pa = 10

V = 900

Put all the above values in equation 2 we get,

⇒   = – × 40

⇒   = – 3600

This is the value of rate of decrease of volume.