Boyles law states that if the temperature of a gas remains constant, then PV=c,

Question

Boyles law states that if the temperature of a gas remains constant, then PV=c, where P=pressure, V=volume, and c is constant. Given a quantity of gas at constant temperature, if V is decreasing at a rate of 8 in^3/sec, at what rate is P increasing when P=30 lb/in^2 and V=80 in^3? Boyles law states that if the temperature of a gas remains constant, then PV=c, where P=pressure, V=volume, and c is constant. Given a quantity of gas at constant temperature, if V is decreasing at a rate of 8 in^3/sec, at what rate is P increasing when P=30 lb/in^2 and V=80 in^3?

Explanation / Answer

we have,

PV = c

P(-dV/dt) + V(dP/dt) = 0, dV/dt has a negative sign with it as V is decreasing;

So, dP/dt = (P/V)(dV/dt), where dP/dt is the rate of increase of P

or, dP/dt = [(30 lb/in2)/(80 in3)](8 in3/s)

or, dP/dt = 3 lb/in2/s

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