When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV^1.4 = C where C is a constant.
Suppose that at a certain instant the volume is 310cm^3 , and the pressure is 83 kPa (kPa = kiloPascals) and is decreasing at a rate of 8 kPa/minute. At what rate is the volume increasing at this instant?
The volume is increasing at ..... cm^3/min
Suppose that at a certain instant the volume is 310cm^3 , and the pressure is 83 kPa (kPa = kiloPascals) and is decreasing at a rate of 8 kPa/minute. At what rate is the volume increasing at this instant?
The volume is increasing at ..... cm^3/min
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V^1.4 = CP^-1
1.4V^0.4dV/dt = -CP^-2dP/dt
83*310^1.4 = C
1.4V^0.4dV/dt = -83*310^1.4*P^-2dP/dt
1.4*310^0.4dV/dt = 83*310^1.4*83^-2*8
1.4*310^0.4dV/dt = 296.4273
dV/dt = 21.34 cm^3/min
1.4V^0.4dV/dt = -CP^-2dP/dt
83*310^1.4 = C
1.4V^0.4dV/dt = -83*310^1.4*P^-2dP/dt
1.4*310^0.4dV/dt = 83*310^1.4*83^-2*8
1.4*310^0.4dV/dt = 296.4273
dV/dt = 21.34 cm^3/min