JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Heat & Thermodynamics

A bakelite beaker has volume capacity of 500 cc at

3 0^{\circ} C

. When it is partially filled with

V_{m}

volume (at

3 0^{\circ} C

) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If

γ_{(beaker)} = 6 \times 1 0^{- 6}^{\circ} C^{- 1}

and

γ_{(mercury)} = 1.5 \times 1 0^{- 4}^{\circ} C^{- 1}

, where

γ

is the coefficient of volume expansion, then

V_{m}

(in cc) is close to ______.

Answer: 20

Solution

The unfilled space stays constant only if the mercury expands by exactly as much as the beaker's capacity does for every temperature change,

V_{b} γ_{b} Δ T = V_{m} γ_{m} Δ T

. Cancelling

Δ T

V_{m} = \frac{V _{b} γ _{b}}{γ _{m}} = \frac{500 \times 6 \times 1 0 ^{- 6}}{1.5 \times 1 0 ^{- 4}} = 20

cc.

JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Integer answer

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