SATHEE: Thermodynamics Question 253

Thermodynamics Question 253

Question: The relation between U, P and V for an ideal gas in an adiabatic process is given by relation $U = a + b P V .$ Find the value of adiabatic exponent $(γ)$ of this gas.

Options:

A) $\frac{b + 1}{b}$

B) $\frac{b + 1}{a}$

C) $\frac{a + 1}{b}$

D) $\frac{a}{a + b}$

Show Answer

Answer:

Correct Answer: A

Solution:

[a] $U = a + b P V$ ..(i)

In adiabatic change, $d U = - d W = \frac{n R}{γ - 1} (T_{2} - T_{1}) = \frac{n R}{γ - 1} (d T)$

$\Rightarrow U = \int_{}^{} d U = \frac{n R}{γ - 1} \int_{}^{} d T$

$o r U = (\frac{n R}{γ - 1}) T + a = \frac{P V}{γ - 1} + a$ .(ii)

Where a is the constant of integration.

Comparing (1) and (2), we get $b = \frac{1}{γ - 1} \Rightarrow γ = \frac{b + 1}{b} .$

Thermodynamics Question 253

Question: The relation between U, P and V for an ideal gas in an adiabatic process is given by relation $U = a + b P V .$ Find the value of adiabatic exponent $(γ)$ of this gas.

Options:

Answer:

Solution:

Engineering Preparation

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NCERT Books & Solutions

Important Resources

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Syllabus

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Sample Mock Test

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NCERT Exercise Video Solution

Thermodynamics Question 253

Question: The relation between U, P and V for an ideal gas in an adiabatic process is given by relation U=a+bPV. Find the value of adiabatic exponent (γ) of this gas.

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: The relation between U, P and V for an ideal gas in an adiabatic process is given by relation $U = a + b P V .$ Find the value of adiabatic exponent $(γ)$ of this gas.