The pressure P₁ and density d₁ of diatomic gas $(γ = \frac{7}{5})$ changes suddenly to P₂(>P₁) and d₂ respectively during an adiabatic process. The temperature of the gas increases and becomes ________times of its initial temperature. (given $\frac{d_{2}}{d_{1}} = 32)$

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Vishal Baghel | Contributor-Level 10

2 months ago

For adiabatic process – PV^Y= const

$T_{1} {V_{1}}^{Y - 1} = T_{2} V_{2}^{Y - 1}$

$\frac{T_{2}}{T_{1}} = {(\frac{v_{1}}{v_{2}})}^{Y - 1} = {(\frac{d_{2}}{d_{1}})}^{Y - 1} = {(32)}^{(\frac{7}{5} - 1)} = {(32)}^{2 / 5}$

$= {(2)}^{2} = 4$

For adiabatic process – PVY = const <math> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msup> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>Y</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msubsup> <mrow> <mi>V</mi> </mrow> <mrow> <mn>2</mn> </mrow> <mrow> <mi>Y</mi> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </math> <math> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>Y</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>d</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>d</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>Y</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <mn>3</mn> <mn>2</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mrow> <mo> (</mo> <mrow> <mfrac> <mrow> <mn>7</mn> </mrow> <mrow> <mn>5</mn> </mrow> </mfrac> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <mn>3</mn> <mn>2</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> <mo>/</mo> <mn>5</mn> </mrow> </msup> </mrow> </math> <math> <mrow> <mo>=</mo> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <mn>2</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>4</mn> </mrow> </math>

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The pressure P₁ and density d₁ of diatomic gas $(γ = \frac{7}{5})$ changes suddenly to P₂(>P₁) and d₂ respectively during an adiabatic process. The temperature of the gas increases and becomes ________times of its initial temperature. (given $\frac{d_{2}}{d_{1}} = 32)$

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The pressure P1 and density d1 of diatomic gas ( γ = 7 5 ) changes suddenly to P2(>P1) and d2 respectively during an adiabatic process. The temperature of the gas increases and becomes ________times of its initial temperature. (given d 2 d 1 = 3 2 )

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The pressure P₁ and density d₁ of diatomic gas $(γ = \frac{7}{5})$ changes suddenly to P₂(>P₁) and d₂ respectively during an adiabatic process. The temperature of the gas increases and becomes ________times of its initial temperature. (given $\frac{d_{2}}{d_{1}} = 32)$