Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 11-science Answered

pls           show    mathematically  or say prove it ( explaining  step  by step)  mathematically that   "density of solid/liquid  decreases  with rise in temperature".        
Asked by ppratim02 | 08 Jan, 2016, 08:37: PM
answered-by-expert Expert Answer
When a given mass of a solid or a liquid is heated, it generally expands i.e., its volume increases. As density varies inversely as the volume, therefore, density of a solid or a liquid would decrease on heating.
Suppose V is the volume of a certain mass M of a solid or liquid at temperature T. Let the volume of the same mass increase to V', when the temperature is raised by a small amount begin mathsize 14px style triangle straight T end style.
If γ is coefficient of volume expansion of the solid/liquid, then
V'=V(1+γbegin mathsize 14px style triangle straight T end style)       ... (1)
If begin mathsize 14px style straight rho end style is the density of the soild/liquid at temperature T
begin mathsize 14px style straight rho apostrophe end style is the density of the soild/liquid at temperature begin mathsize 14px style left parenthesis straight T plus triangle straight T right parenthesis end style
then,
begin mathsize 14px style straight rho equals straight M over straight V or space straight V equals straight M over straight rho and space straight rho apostrophe equals fraction numerator straight M over denominator straight V apostrophe end fraction or space straight V apostrophe equals fraction numerator straight M over denominator straight rho apostrophe end fraction Putting space in space eqn left parenthesis 1 right parenthesis comma space we space get comma fraction numerator straight M over denominator straight rho apostrophe end fraction equals straight M over straight rho left parenthesis 1 plus straight gamma triangle straight T right parenthesis or space straight rho apostrophe equals fraction numerator straight rho over denominator left parenthesis 1 plus straight gamma triangle straight T right parenthesis end fraction equals straight rho space left parenthesis 1 plus straight gamma triangle straight T right parenthesis to the power of negative 1 end exponent Expanding space binomically comma space we space get comma space straight rho apostrophe equals straight rho space left parenthesis 1 minus straight gamma triangle straight T right parenthesis therefore straight rho apostrophe equals straight rho comma space straight i. straight e. comma space the space density space of space straight a space solid divided by liquid space decreases space with space rise space in space temperature. end style
Answered by Faiza Lambe | 11 Jan, 2016, 03:33: PM
CBSE 11-science - Physics
Asked by shubhamgoyal1722 | 15 Dec, 2020, 11:18: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by pgskgokul | 06 Jul, 2020, 02:50: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by abhilashkulgude111 | 07 Jun, 2019, 09:05: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by Topperlearning User | 13 Apr, 2015, 03:19: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by Topperlearning User | 13 Apr, 2015, 03:20: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×