Density in a Physics Question??? Please help...?

Question

At a temperature of 0 degrees celsius, the mass and volume of a fluid are 825 kg and 1.17 m^3. The coefficient of volume expansion is 1.26 x 10^-3 (degrees celsius)^-1. (a) what is the density of fluid at this temperature? (b) What is the density of the fluid when the temperature has risen to 20.0 degrees celsius?

My Approach:

(a) d = m/v = 825 kg/ 1.17m^3 = 705 kg/m^3

(b) d = (705 kg/m^3)(1.26 x 10^-3) (20 degrees celsius) = 17.8 kg/m^3

I really don't know what equation to use b/c my textbook is horrible in explaining these types of random problems! I appreciate all the help I can get

Answer 1

density is mass per unit volume, so part (a) is correct.

the coefficient of volume expansion (I'll represent with the letter B) is:

B = (1/V)*dV/dT
where dV is the change in volume and dT is the change in temp.

In your problem we need to find the volume at the new temp.
so rearranging this equation:
dV = B*V*dT
it might be easier if we write dV as the difference between final volume and initial volume, likewise for dT:

V2 - V1 = B*V1*(T2-T1)
so we need to find V2:
V2 = V1*[1+B*(T2-T1)]
V2 = 1.17 * [1+ [1.26*10^-3]*(20-0)] = 1.2 (rounded)

d = m/v = 825 / V2 = 688 kg/m^3

this is a more reasonable answer than what you have.

Answer 2

To get your quantity, you'll want a bathtub with without delay aspects. Fill it adequate that you'll thoroughly immerse your self into it and mesaure how severe the water rises. That shows how a lot you displace the water. Now, enable's say the bath is two meter through 1 million meter and also you develop the water factor through .25 meters (those figures are probable not even close), then your quantity will be 2 * a million * .25 or .5 cubic meters. Get your weight (to make it user-friendly i will imagine that you weigh 100KG) and divde that through your quantity or one hundred/.5 which supplies 2 hundred kg/cubic meter. you may then get the density of the different aspects (verify your physics books or do a search for on the information superhighway) and end your project.

Answer 3

(a) looks OK
(b) does not. The coefficient of volume expansion represents the CHANGE in volume, not the volume. For a 20ºC change, the change in volume is only about 2.5%, so the density decreases by a similar amount