Question

Volume of the bulb of a mercury thermometer at 00C is ‘V’0 and area of cross - section of the capillary tube is ‘A0’ coefficient of linear expansion of glass is αg/0Cand the coefficient cubical expansion of Mercury is γHg/0C. If the mercury fills the bulb at 00C, the length of mercury column in capillary tube at t0C is

 

A)  V0t(γHg+3αg)A0(1+2αgt)

B)  V0t(γHg−3αg)A0(1+2αgt)

C)  V0t(γHg−3αg)A0

D)  V0tγHgA0

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Answer 1

Given that,

Volume of mercury = V₀

Area of capillary tube = A₀

Initial temperature = 0°C

Final temperature = t°C

Linear expansion of glass at 0°C $=\alpha_{g}$

Cubical expansion of Mercury $=\gamma_{Hg}$

For mercury,

Expansion of mercury  =$V_{0}\gamma_{Hg}\DeltaT$

Put the value of $\Delta T$

Expansion of mercury  =$V_{0}\gamma_{Hg}(t-0)$

Expansion of mercury  =$V_{0}\gamma_{Hg}t$

For glass,

Expansion of glass  =$V_{0}3\alpha_{g}t$

We know that,

Apparent expansion is equal to the area multiply by length.

$\text{apparent expansion}=A_{0}\times l$

We need to calculate the length of mercury column

Using apparent expansion

$\text{apparent expansion}=V_{0}\gamma_{Hg}t-V_{0}3\alpha_{g}t$

Put the value into the formula

$A_{0}\times l=V_{0}t(\gamma_{Hg}-3\alpha_{g})$

$l=\dfrac{V_{0}t(\gamma_{Hg}-3\alpha_{g})}{A_{0}}$

Hence,  The length of mercury column is $\dfrac{V_{0}t(\gamma_{Hg}-3\alpha_{g})}{A_{0}}$

(C) is correct option

Answer 2

Explanation:

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