An ideal gas undergoes a thermodynamic process in which internal energy <math> <mo>(</mo> <mi>U</mi> <mo>)</mo> </math> of the gas depends on pressure <math> <mo>(</mo> <mi>P</mi> <mo>)</mo> </math> of the gas as <math> <mi> </mi> <mo>=</mo> <mi> </mi> <mi>a</mi> <msup> <mrow> <mrow> <mi>P</mi> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> </mrow> </mrow> </msup> </math> , where a is a positive constant. Assuming gas to be monoatomic, the molar heat capacity of the gas for given process will be

U = a P 4 P V γ - 1 = a P 4 P - 3 V = a γ - 1 P V - 1 / 3 = c o n s t a n t C o m p a r i n g w i t h P V x = c o n s t a n t x = - 1 3 C = R γ - 1 + R 1 - x = R 5 3 - 1 + R 1 + 1 3 = 3 R 2 + 3 R 4 C = 9 R 4

An ideal gas undergoes a thermodynamic process in which internal energy <math> <mo>(</mo> <mi>U</mi> <mo>)</mo> </math> of the gas depends on pressure <math> <mo>(</mo> <mi>P</mi> <mo>)</mo> </math> of the gas as <math> <mi> </mi> <mo>=</mo> <mi> </mi> <mi>a</mi> <msup> <mrow> <mrow> <mi>P</mi> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> </mrow> </mrow> </msup> </math> &nbsp;, where a is a positive&nbsp;&nbsp; constant. Assuming gas to be monoatomic, the molar heat capacity of the gas for given process will be

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Physics Thermodynamics Physics Class 11th Thermodynamics

An ideal gas undergoes a thermodynamic process in which internal energy $(U)$ of the gas depends on pressure $(P)$ of the gas as $= a P^{4}$ , where a is a positive constant. Assuming gas to be monoatomic, the molar heat capacity of the gas for given process will be

Option 1 -

$\frac{3 R}{4}$

Option 2 -

$\frac{2 R}{3}$

Option 3 -

$\frac{9 R}{4}$

Option 4 -

$\frac{4 R}{9}$

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Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 3

Detailed Solution:

$U = a P^{4}$

$\frac{P V}{γ - 1} = a P^{4}$

$P^{- 3} V = a (γ - 1)$

$P V^{- 1 / 3} = c o n s t a n t$

$C o m p a r i n g w i t h P V^{x} = c o n s t a n t$

$x = - \frac{1}{3}$

$C = \frac{R}{γ - 1} + \frac{R}{1 - x} = \frac{R}{\frac{5}{3} - 1} + \frac{R}{1 + \frac{1}{3}} = \frac{3 R}{2} + \frac{3 R}{4}$

$C = \frac{9 R}{4}$

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An ideal gas undergoes a thermodynamic process in which internal energy $(U)$ of the gas depends on pressure $(P)$ of the gas as $= a P^{4}$ , where a is a positive constant. Assuming gas to be monoatomic, the molar heat capacity of the gas for given process will be

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An ideal gas undergoes a thermodynamic process in which internal energy ( U ) of the gas depends on pressure ( P ) of the gas as = a P 4 , where a is a positive constant. Assuming gas to be monoatomic, the molar heat capacity of the gas for given process will be

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An ideal gas undergoes a thermodynamic process in which internal energy $(U)$ of the gas depends on pressure $(P)$ of the gas as $= a P^{4}$ , where a is a positive constant. Assuming gas to be monoatomic, the molar heat capacity of the gas for given process will be