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Please help me with this problem.

# A vertical column of liquid 50 cm long at 50 degree Celsius balances another column of same liquid 60 cm long at 100 degree Celsius. What is the coefficient of absolute expansion of the liquid?

I solved it in the following way:

Pressure exerted by 50 cm of liquid at 50 degree Celsius = Pressure exerted by 60 cm of liquid at 100 degree Celsius.

Hence, (h1)(d1)g = (h2)(d2)g

50 x d1 x g = 100 x d2 x g

d1 = 2 x d2 -------- (1)

We know that d1 = d2[1 + r(dt)] --------- (2)

Where d1 = density at T1 temperature

d2 = density at T2 temperature(Here T1<T2)

r = coefficient of cubical expansion of the liquid

dt = T2 – T1

Substituting (1) in (2) we get,

2 x d2 = d2[1 + (r x 50)]

By solving we get,

r = 0.004 / deg Celsius

But the answer given in my book is 0.005/ deg Celsius. Please advice.

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# Homework Help: Columns of liquids at different temperuatures

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