Need help with Calculus 1 question?
2020-11-03 8:40 am
A sample of gas is placed in a cylindrical piston. At the beginning of the experiment, the gas occupies a volume of 550 cm^3, and has a pressure of 100 kPa. The piston is slowly compressed, decreasing the volume of the gas at a rate of 50 cm^3/min. How quickly will the pressure of the gas change when the volume is 100 cm^3? [Use Boyles Law PV=constant]
回答 (1)
2020-11-03 10:53 am
✔ 最佳答案
Initial: P₁ = 100 kPa, V₁ = 550 cm³Final: P₂ = ? kPa, V₂ = 100 cm³
Boyle's law: PV = constant ⇒ P₁V₁ = P₂V₂
Then, P₂ = P₁V₁/V₂
Final pressure, P₂ = 100 × 550 / 100 kPa = 550 kPa
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PV = constant
d(PV)/dt = d(constant)/dt
P(dV/dt) + V(dP/dt) = 0
When V = 100 cm³, P = 550 kPa and dV/dt = -50 cm³:
550(-50) + 100(dP/dt) = 0
dP/dt = 275 kPa/min
收錄日期: 2021-04-23 23:08:17
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