it is observed that 55.50 ml of water at 20°c completely fills a container to the brim. when the container and the water are heated to 60°c, 0.35 g of water is lost. (a) what is the coefficient of volume expansion of the container? (b) what is the most likely material of the container? density of water at 60°c is 0.98324 g/ml.

Volume of water that spilled out 
= (0.35) * (0.98324) mL 
= 0.3441 mL 

Thus, the original volume 
55.50 mL increased to 
55.8441 mL 

V(t) = Vo [1 + γ(60.0 - 18.7)] 
=> coefficient of volume expansion, 
γ = (Vt - Vo) / [Vo * 41.3] 
= (0.3441) / [(55.50) (41.3) 

 = 1.5012 x10^-4

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: