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In: Physics

A liquid has a density at 289K of 955kg/m^3. Its(volume) thermal expansion coefficient is 1.05E-3/K. What...

A liquid has a density at 289K of 955kg/m^3. Its(volume) thermal expansion coefficient is 1.05E-3/K. What is its density at 316K? Answer 929 kg/m^3 I'd appreciate explanation ! Thank you :)

Solutions

Expert Solution

Volume thermal expansion coefficient = = 1.05 x 10-3 K-1

Initial temperature of the liquid = T1 = 289 K

Initial density of the liquid = 1 = 955 kg/m3

Initial volume of the liquid = V1

New temperature of the liquid = T2 = 316 K

New density of the liquid =  2

New volume of the liquid = V2

Change in volume of the liquid = V

V = V1(T2 - T1)

V2 = V1 + V

V2 = V1 + V1(T2 - T1)

V2 = V1(1 + (T2 - T1))

The mass of the liquid remains same

Mass of the liquid = M

M = 1V1 = 2V2

1V1 = 2V2

1V1 = 2V1(1 + (T2 - T1))

1 = 2(1 + (T2 - T1))

955 = 2(1 + (1.05x10-3)(316 - 289))

2 = 928.67 kg/m3

Density of the liquid at 316 K = 928.67 kg/m3


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