Q. 6

# The pressure p an

Given pv1.4 = constant and the decrease in v is .

Hence, we have Δv = –0.005v

We have pv1.4 = constant

Taking log on both sides, we get

log(pv1.4) = log(constant)

log p + log v1.4 = 0 [ log(ab) = log a + log b]

log p + 1.4 log v = 0 [ log(am) = m log a]

On differentiating both sides with respect to v, we get  We know     Recall that if y = f(x) and Δx is a small increment in x, then the corresponding increment in y, Δy = f(x + Δx) – f(x), is approximately given as Here, and Δv = –0.005v Δp = (–1.4p)(–0.005)

Δp = 0.007p

The percentage error is, Error = 0.007 × 100%

Error = 0.7%

Thus, the error in p corresponding to the decrease in v is 0.7%.

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