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 1000 cm3, the pressure is 80 kPa, and the pressure is increasing at a rate of 20 kPa/min. At what rate is the volume decreasing at this instant?

Question

Mathematics

Rodrigo Mcclain

14 May, 13:57

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 1000 cm3, the pressure is 80 kPa, and the pressure is increasing at a rate of 20 kPa/min. At what rate is the volume decreasing at this instant?

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Cooper Gonzalez · Answer 1

The volume is decreasing at a rate of 250 cm^3/min

Step-by-step explanation:

From Boyle's law, the relationship between pressure (P) and volume (V) is inverse in which increase in one quantity (P) leads to a corresponding decrease in the other quantity (V).

Pressure at a certain instant (time) = 80 kPa

Rate at which pressure is increasing = 20 kPa/min

Time required for this increase = pressure : rate = 80 : 20 = 4 min

Volume = 1000 cm^3

Rate at which volume is decreasing at the same time pressure is increasing = 1000 : 4 = 250 cm^3/min