Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of 57 0C is drunk. You can take body (tooth) temperature to be 370 C and α = 1.7× 10-5 / 0C , bulk modulus for copper = 140 × 109 N/m2.

This is a long answer type question as classified in NCERT ExemplarDecrease in temperature ? t = 57-37= 200CCoefficient of linear expansion α = 1.7 × 10 - 5 / oCBulk modulus for copper B = 140 × 10 9 N / m 2 Coefficient of cubical expansion γ = 3 α = 5.1 × 10 - 5 / ° C Let initial volume of the cavity be V and its volume increases by ? V due to increase in temperature. ? V = γ V ? t ? V V = γ ? t Thermal stress produced = B × v o l u m e t r i c s t r a i n = B × ? V V = B γ ? t = 140 × 10 9 × 5.1 × 10 - 5 × 20 = 1428 × 10 8 N / m 2

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Thermal Properties of Matter physics ncert solutions class 11th Physics Class 11th Physics NCERT Exemplar Solutions Class 11th Chapter Eleven

Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of 57 ⁰C is drunk. You can take body (tooth) temperature to be 37⁰ C and α = 1.7× 10^-5 / ⁰C , bulk modulus for copper = 140 × 10⁹ N/m².

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Payal Gupta | Contributor-Level 10

4 months ago

This is a long answer type question as classified in NCERT Exemplar

Decrease in temperature $? t$ = 57-37= 20⁰C

Coefficient of linear expansion $α$ = 1.7 $\times 10^{- 5} /$ ^oC

Bulk modulus for copper B = 140 $\times 10^{9} N / m^{2}$

Coefficient of cubical expansion $γ$ = 3 $α$ = 5.1 $\times 10^{- 5} / ° C$

Let initial volume of the cavity be V and its volume increases by $? V$ due to increase in temperature.

$? V = γ V ? t$

$\frac{? V}{V} = γ ? t$

Thermal stress produced = B $\times v o l u m e t r i c s t r a i n$

= B $\times \frac{? V}{V} = B γ ? t$

= 140 $\times 10^{9} \times 5.1 \times 10^{- 5} \times 20$

= 1428 $\times 10^{8} N / m$ ²

This is a long answer type question as classified in NCERT ExemplarDecrease in temperature <math> <mo>? </mo> <mi>t</mi> </math> = 57-37= 200CCoefficient of linear expansion <math> <mi>α</mi> </math> = 1.7 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </mrow> </msup> <mo>/</mo> </math> oCBulk modulus for copper B = 140 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>9</mn> </mrow> </mrow> </msup> <mi>N</mi> <mo>/</mo> <msup> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </math> Coefficient of cubical expansion <math> <mi>γ</mi> </math> = 3 <math> <mi>α</mi> </math> = 5.1 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </mrow> </msup> <mo>/</mo> <mo>°</mo> <mi>C</mi> </math> Let initial volume of the cavity be V and its volume increases by <math> <mo>? </mo> <mi>V</mi> </math>  due to increase in temperature. <math> <mo>? </mo> <mi>V</mi> <mo>=</mo> <mi>γ</mi> <mi>V</mi> <mo>? </mo> <mi>t</mi> </math> <math> <mfrac> <mrow> <mrow> <mo>? </mo> <mi>V</mi> </mrow> </mrow> <mrow> <mrow> <mi>V</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mi>γ</mi> <mo>? </mo> <mi>t</mi> </math> Thermal stress produced = B <math> <mo>×</mo> <mi>v</mi> <mi>o</mi> <mi>l</mi> <mi>u</mi> <mi>m</mi> <mi>e</mi> <mi>t</mi> <mi>r</mi> <mi>i</mi> <mi>c</mi> <mi> </mi> <mi>s</mi> <mi>t</mi> <mi>r</mi> <mi>a</mi> <mi>i</mi> <mi>n</mi> </math> = B <math> <mo>×</mo> <mfrac> <mrow> <mrow> <mo>? </mo> <mi>V</mi> </mrow> </mrow> <mrow> <mrow> <mi>V</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mi>B</mi> <mi>γ</mi> <mo>? </mo> <mi>t</mi> </math> = 140 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>9</mn> </mrow> </mrow> </msup> <mo>×</mo> <mn>5.1</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </mrow> </msup> <mo>×</mo> <mn>20</mn> </math> = 1428 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>8</mn> </mrow> </mrow> </msup> <mi>N</mi> <mo>/</mo> <mi>m</mi> </math> 2

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Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of 57 ⁰C is drunk. You can take body (tooth) temperature to be 37⁰ C and α = 1.7× 10^-5 / ⁰C , bulk modulus for copper = 140 × 10⁹ N/m².

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