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Show that density varies with temperatur...

Show that density varies with temperature as `rho_(2)=rho_(1)(1-gammaDeltaT)` for small change in temperature.

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`rho_(1)=(m)/(V_(1)) and rho_(2)=(m)/(V_(2))`
`V_(2)=V_(1)(1+gammaDeltaT)`
`:. rho_(2)=(rho_(1))/(v_(1)(1+gammaDeltaT))`
`rArr rho_(2)=(rho_(1))/((1+gamma DeltaT))`
`rArr rho_(2)=(rho_(1))/((1+gammaDeltaT))`
`rArr rho_(2)=((rho_(1)(1-gamma)DeltaT))/((1+gamma DeltaT)(1-gamma DeltaT))`
`rArr rho=(rho_(1)(1-gammaDeltaT))/((1-gamma^(2)DeltaT^(2)))`
Usually `gamma` is very small
` gamma^(2) lt lt 1`
`1-gamma^(2) DeltaT^(2)~~1`
`rho_(2)=rho_(1)(1-gammaDeltaT)`
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CENGAGE PHYSICS-HEAT AND TEMPERATURE -MANDATORY EXERCISE (Exercise Set III)
  1. Give scientific reasons for the following. ice is slippery.

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  2. Give scientific reasons for the following. Water in an earthen pot ...

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  3. The coefficient of linear expansion for brass is 0.000018//^(@)C. Expl...

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  4. The relation between beta and gamma of a solid is

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  5. When ice is converted to water changes.

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  6. When water is heated from 0^@C, its volume

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  7. The density of water is maximum at:

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  8. A plate with a hole is heated. The diameter of the hole

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  9. The pendulum of a clock is made of a thin iron rod. On a hot day the c...

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  10. Stars A and B appear to be blue and red in colour, respectively. Then ...

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  11. While making homemade ice cream, salt is added to the ice in the conta...

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  12. Matter expands on heating. Explain

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  13. What is the temperature at the bottom of deep lakes and seas?

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  14. Explain the importance of anomalous expansion of water to maintain the...

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  15. How does a bimetallic strip function?

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  16. The length of a piece of wood is measured with a metallic scale on a h...

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  17. The length of a piece of metal is measured with a wooden scale on a ho...

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  18. The coefficient of linear expansion for a material is 2 xx 10^(-5)//^(...

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  19. Show that density varies with temperature as rho(2)=rho(1)(1-gammaDelt...

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  20. Thermal capacity of an object depends on

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