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Math

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At a temperature of 20°C, the volume V (in liters) of 1.33 g of O2 is related to its pressure p (in atmospheres) by the formula
V(p) = 1/p

(a) What is the average rate of change of V with respect to p as p increases from p = 7 to p = 8?
L/atm

(b) What is the rate of change to V with respect to p when p = 7?
L/atm

  • Math - ,

    V(p) = 1/p
    V(6) = 1/6
    V(7) = 1/7
    ΔV = V(7) - V(6) = 1/7 - 1/6 = -1/42
    Δp = 7 - 6 = 1
    a)Average rate of change:
    ΔV/Δp = (-1/42)/1 = -1/42 Liter/atmosphere

  • Math - ,

    V(p) = 1/p
    V(6) = 1/6
    V(7) = 1/7
    ΔV = V(7) - V(6) = 1/7 - 1/6 = -1/42
    Δp = 7 - 6 = 1
    a)Average rate of change:
    ΔV/Δp = (-1/42)/1 = -1/42 Liter/atmosphere
    Actual rate of change
    dV/dp = -1/p²
    At p = 6
    dV/dp = -1/6² = -1/36 L/atm

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