The temperature q at the junction of two insulating sheets,having thermal resistances R₁ and R₂ as well top and bottom temperatures q₁ and q₂ (as shown in figure) is given by

Correct Option - 1


Detailed Solution:

taking θ₁ > θ₂

Heat current = $\frac{{\theta }_1-\theta }{R_1}=\frac{\theta -{\theta }_2}{R_2}\Rightarrow \frac{{\theta }_1}{R_1}+\frac{{\theta }_2}{R_2}=\theta \left(\frac{1}{R_1}+\frac{1}{R_2}\right)$

$\Rightarrow \theta =\frac{{\theta }_1{R}_2+{\theta }_2{R}_1}{R_1+R_2}$

 

<p>taking θ₁ &gt; θ₂</p><p>Heat current =&nbsp;<math><mrow><mfrac><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><mi>θ</mi></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>θ</mi><mo>−</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac><mo>⇒</mo><mfrac><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac><mo>+</mo><mfrac><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac><mo>=</mo><mi>θ</mi><mrow><mo> (</mo><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></math></p><p><math><mrow><mo>⇒</mo><mi>θ</mi><mo>=</mo><mfrac><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac></mrow></math></p><div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1755148443phpWIw7oS.jpeg" alt="" width="218" height="118" loading="lazy"></picture></div></div><p>&nbsp;</p>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment