Consider the efficiency of carnot’s engine is given by $\eta =\frac{\alpha \beta }{sin\theta }loge\frac{\beta x}{kT},$ where and are constants. If T is temperature, k is Boltzmann constant, is angular displacement and x has the dimensions of length. Then, choose the incorrect option

<p>Efficiency&nbsp;<math><mrow><mi>η</mi><mo>=</mo><mfrac><mrow><mi>α</mi><mi>B</mi></mrow><mrow><mi>s</mi><mi>i</mi><mi>n</mi><mi>θ</mi></mrow></mfrac><mi>l</mi><mi>o</mi><msub><mrow><mi>g</mi></mrow><mrow><mi>e</mi></mrow></msub><mfrac><mrow><mi>B</mi><mi>x</mi></mrow><mrow><mi>k</mi><mi>T</mi></mrow></mfrac><mtext></mtext><mtext></mtext><mi>α</mi><mo>, </mo><mi>B</mi><mo>→</mo><mi>c</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi>s</mi></mrow></math></p><p>As, energy&nbsp;<math><mrow><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mi>k</mi><mi>T</mi><mo>⇒</mo></mrow></math>&nbsp;Dimension of Bx = Dimension of energy</p><p>So Dimension as of B = Dimension of ‘F’</p><p>Dimension of F1</p><p>Dimension of&nbsp;<math><mrow><mrow><mo> (</mo><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>α</mi></mrow></mfrac></mrow><mo>)</mo></mrow><mi>x</mi><mo>=</mo></mrow></math>&nbsp;Dimension of energy</p>

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