Answer:
-90cm³/min
Explanation:
The equation is:
[tex] P*V = C [/tex] (1)
Where P: is the pressure, V: is the volume, and C: is a constant.
To find the rate at which the volume decrease, we need to derivate equation (1):
[tex] P\cdot \frac{dV}{dt} + \frac{dP}{dt}*V = \frac{dC}{dt} [/tex] (2)
From equation (2) we have:
P = 200 kPa
V = 900 cm³
[tex] \frac{dP}{dt} = 20 kPa/min [/tex]
[tex] \frac{dC}{dt} = 0 [/tex]
Hence, by entering the values above in equation (2), we have:
[tex]200 kPa\cdot \frac{dV}{dt} + 20 kPa/min* 900 cm^{3} = 0 [/tex]
[tex]\frac{dV}{dt} = - \frac{20 kPa/min* 900 cm^{3}}{200 kPa} = - 90 cm^{3}/min[/tex]
Therefore, the rate at which the volume is decreasing is -90cm³/min.
I hope it helps you!
