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Effect of Temperature on Upthrust

In this article we are going to discuss about the Effect of Temperature on Upthrust as the temperature of a body which is changed.

We know that whenever a body is immersed in a liquid, partially or completely, its weight appears to be less in comparison to its weight in air.

This is because of the force applied by the liquid on the body in vertically upward direction (opposite to the direction of weight), which is called UPTHRUST or BUOYANT FORCE, given by :-

F = V_sρ_L g ……….(1)

Where,

Vs = Volume of the solid body immersed in the liquid

ρ_L= Density of the liquid &

g = acceleration due to gravity.

The apparent weight (weight when immersed in the liquid), W_app of the body is given by :-

W_app = W – F ……….(2)

Where W is the weight of the body as measured in air.

Now as we increase the temperature, Vs increases ( volume expansion ) and ρ_Ldecreases ( variation in density with temperature ) .

So upthrust F, may increase or may decrease or may remains the same, depending on the factor which dominates [from equation (1)].

Let us discuss these factors one by one. From equation (1) :-

$\displaystyle F={{V}_{S}}{{\rho }_{L}}g$ ……….(3)

Now let the temperature changes by ΔT, then new upthrust F’

$\displaystyle {{F}^{'}}=V_{_{S}}^{'}\rho _{_{L}}^{'}g$ ……….(4)

Dividing equation (4) by equation (3), we get :-

$\displaystyle \Rightarrow \frac{{{F}^{'}}}{F}=\frac{V_{_{S}}^{'}\rho _{_{L}}^{'}g}{{{V}_{S}}{{\rho }_{L}}g}$

$\displaystyle \Rightarrow \frac{{{F}^{'}}}{F}=\frac{V_{_{S}}^{'}\rho _{_{L}}^{'}}{{{V}_{S}}{{\rho }_{L}}}=\frac{{{V}_{S}}(1+{{\gamma }_{S}}\Delta T)}{{{V}_{S}}}\times \frac{1}{{{\rho }_{L}}}\frac{{{\rho }_{L}}}{(1+{{\gamma }_{L}}\Delta T)}$

$\displaystyle \Rightarrow {{F}^{'}}=F\frac{(1+{{\gamma }_{S}}\Delta T)}{(1+{{\gamma }_{L}}\Delta T)}$ ……….(5)

Now if [from eq. (5) and (2)]

(a) γ_S > γ_L , then F’ > F ⇒ W’_app < W_app

(b) γ_S < γ_L , then F’ < F ⇒ W’_app > W_app and if

(c) γ_S = γ_L , then F’ = F ⇒ W’_app = W_app

Next Topic :- Bimetallic Strip

Previous Topic :- Thermal Stress

Effect of Temperature on Upthrust

Effect of Temperature on Upthrust

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