## 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?

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

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.