Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P P and volume V V satisfy the equation P V = C PV=C, where C C is a constant. Suppose that at a certain instant the volume is 1000 cm 3 1000 cm3, the pressure is 80 kPa 80 kPa, and the pressure is increasing at a rate of 40 kPa/min 40 kPa/min. At what rate is the volume decreasing at this instant?

Question

Physics

Ariel Lewis

17 September, 04:04

Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P P and volume V V satisfy the equation P V = C PV=C, where C C is a constant. Suppose that at a certain instant the volume is 1000 cm 3 1000 cm3, the pressure is 80 kPa 80 kPa, and the pressure is increasing at a rate of 40 kPa/min 40 kPa/min. At what rate is the volume decreasing at this instant?

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Answers (1)

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Kamila Drake · Answer 1

the volume decreases at the rate of 500cm³ in 1 min

Explanation:

given

v = 1000cm³, p = 80kPa, Δp/t = 40kPa/min

PV=C

vΔp + pΔv = 0

differentiate with respect to time

v (Δp/t) + p (Δv/t) = 0

(1000cm³) (40kPa/min) + 80kPa (Δv/t) = 0

40000 + 80kPa (Δv/t) = 0

Δv/t = - 40000/80

= - 500cm³/min

the volume decreases at the rate of 500cm³ in 1 min