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Question
The coefficient of apparent expansion of mercury in a glass vessel is 153×10−6/∘C and in a steel vessel is 144×10−6/∘C. If α for steel is then, that of glass is 12×10−6/∘C.then that of glass is
The coefficient of apparent expansion of mercury in a glass vessel is 153×10−6/∘C and in a steel vessel is 144×10−6/∘C. If α for steel is then, that of glass is 12×10−6/∘C.then that of glass is
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Solution
The correct option is D 9×10−6/∘C.
Weknowthatγreal=γapparent+γvesselSo,(γapp+γvessel)glass=(γapp+γvessel)steel(∴γrealissameinbothcases)or153×10−6+(γvessel)glass=144×10−6+(γ_{vessel})_{steel}Further(γ_vessel)_{steel}=3α=3×(12×10−6)=36×10−6/∘C∴153×10−6+(γvessel)glass=144×10−6+36×10−6Solvingweget(γ_{vessel})_{glass}=27×10−6/∘C(γ_{vessel})_{glass}orα=γglass3=9×10−6/∘C
Weknowthatγreal=γapparent+γvesselSo,(γapp+γvessel)glass=(γapp+γvessel)steel(∴γrealissameinbothcases)or153×10−6+(γvessel)glass=144×10−6+(γ_{vessel})_{steel}Further(γ_vessel)_{steel}=3α=3×(12×10−6)=36×10−6/∘C∴153×10−6+(γvessel)glass=144×10−6+36×10−6Solvingweget(γ_{vessel})_{glass}=27×10−6/∘C(γ_{vessel})_{glass}orα=γglass3=9×10−6/∘C
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