At what temperature a gold ring of diameter 6.230cm be heated so that it can be fitted on a wooden bangle of diameter. 6.241cm? Both the diameters have been measured at room temperature (27°C).

(Given : coefficient of linear thermal expansion of gold a_L = 1.4 × 10^-5 K^-1)

<p>According to question, we can write</p><p><span contenteditable="false">&nbsp;<math> <mrow> <mi>d</mi> <mo>=</mo> <msub> <mrow> <mi>d</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mrow> <mo> (</mo> <mrow> <mn>1</mn> <mo>+</mo> <mi>α</mi> <mi>Δ</mi> <mi>T</mi> </mrow> <mo>)</mo> </mrow> <mo>⇒</mo> <mn>6</mn> <mo>.</mo> <mn>2</mn> <mn>4</mn> <mn>1</mn> <mo>=</mo> <mn>6</mn> <mo>.</mo> <mn>2</mn> <mn>3</mn> <mn>0</mn> <mrow> <mo> (</mo> <mrow> <mn>1</mn> <mo>+</mo> <mn>1</mn> <mo>.</mo> <mn>4</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </msup> <mo>×</mo> <mi>Δ</mi> <mi>T</mi> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span></p><p><span contenteditable="false"> <math> <mrow> <mo>⇒</mo> <mi>T</mi> <mo>=</mo> <mn>1</mn> <mn>2</mn> <mn>6</mn> <mo>.</mo> <mn>1</mn> <mn>8</mn> <mo>+</mo> <mn>2</mn> <mn>7</mn> <mo>=</mo> <mn>1</mn> <mn>5</mn> <mn>3</mn> <mo>.</mo> <mn>1</mn> <mn>8</mn> <mo>°</mo> <mi>C</mi> </mrow> </math> </span></p>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment

<p>According to question, we can write</p><p><span class="mathml" contenteditable="false">&nbsp;<math> <mrow> <mi>d</mi> <mo>=</mo> <msub> <mrow> <mi>d</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mrow> <mo> (</mo> <mrow> <mn>1</mn> <mo>+</mo> <mi>? </mi> <mi>? </mi> <mi>T</mi> </mrow> <mo>)</mo> </mrow> <mo>? </mo> <mn>6</mn> <mo>.</mo> <mn>2</mn> <mn>4</mn> <mn>1</mn> <mo>=</mo> <mn>6</mn> <mo>.</mo> <mn>2</mn> <mn>3</mn> <mn>0</mn> <mrow> <mo> (</mo> <mrow> <mn>1</mn> <mo>+</mo> <mn>1</mn> <mo>.</mo> <mn>4</mn> <mo>*</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>? </mo> <mn>5</mn> </mrow> </msup> <mo>*</mo> <mi>? </mi> <mi>T</mi> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span></p><p><span class="mathml" contenteditable="false"> <math> <mrow> <mo>? </mo> <mi>T</mi> <mo>=</mo> <mn>1</mn> <mn>2</mn> <mn>6</mn> <mo>.</mo> <mn>1</mn> <mn>8</mn> <mo>+</mo> <mn>2</mn> <mn>7</mn> <mo>=</mo> <mn>1</mn> <mn>5</mn> <mn>3</mn> <mo>.</mo> <mn>1</mn> <mn>8</mn> <mo>°</mo> <mi>C</mi> </mrow> </math> </span></p>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment