Question

A balloon contains a certain mass of gas whose volume is vcm^3 and whose pressure is p newton per square centimetre and it is known that p and v obeys the law pv=1000. If the volume increases at a rate of 50cm/min, find the rate of change of p when v = 40

Answer 1

Hey Dear,

◆ Answer -

dp/dt = -31.25 N/m²min

● Explaination -

Given that -

pv = 1000

p = 1000/v

Differentiating w.r.t. t,

dp/dt = d(1000/v)/dt

dp/dt = 1000 × -1/v² × dv/dt

dp/dt = -1000/v² × dv/dt

Now, substitute values -

dp/dt = -1000/40² × 50

dp/dt = -31.25 N/m²min

Therefore, rate of change of pressure is -31.25 N/m²min.

Hope this helps you.