A glass vessel is partially filled with mercury and when both are heated together, the volume of the unfilled part of vessel remains constant at all temperature. Find the initial volume (in$$ $$cm3) of mercury if the empty part measures $$34$$ $$cm3$$ Given: αvessel $$=9$$×$$10$$−$$6/$$∘Cγ$$Hg=18$$×$$10$$−$$5/$$∘C

Question

A glass vessel is partially filled with mercury and when both are heated together, the volume of the unfilled part of vessel remains constant at all temperature. Find the initial volume (in$$ $$cm3) of mercury if the empty part measures $$34$$ $$cm3$$  Given: αvessel $$=9$$×$$10$$−$$6/$$∘Cγ$$Hg=18$$×$$10$$−$$5/$$∘C

Infinity Learn · Accepted Answer

$$V1$$→ Initial volume of vessel $$V2$$→ Initial volume of Hg Given $$V1$$−$$V2=34Let$$ temperature is increased by ∆T, $$thenV1$$′−$$V2$$′$$=34$$→as volume of unfilled part remains same. ……..(i)⇒$$V1$$[$$1+3$$αΔT]−$$V2$$[$$1+$$γΔT]$$=34$$⇒$$3V1$$α$$=V2$$γ  ………….(ii)From$$ $$(i) and (ii), $$V2=6cm3$$

Thermal expansion

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Thermal expansion

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A glass vessel is partially filled with mercury and when both are heated together, the volume of the unfilled part of vessel remains constant at all temperature. Find the initial volume (in cm3) of mercury if the empty part measures 34 cm3 Given: αvessel =9×10−6/∘CγHg=18×10−5/∘C

V1→ Initial volume of vessel V2→ Initial volume of Hg Given V1−V2=34Let temperature is increased by ∆T, thenV1′−V2′=34→as volume of unfilled part remains same. ……..(i)⇒V1[1+3αΔT]−V2[1+γΔT]=34⇒3V1α=V2γ ………….(ii)From (i) and (ii), V2=6cm3

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