SATHEE: Thermodynamics and Thermochemistry 1 Question 27

Thermodynamics and Thermochemistry 1 Question 27

30. A monoatomic ideal gas undergoes a process in which the ratio of $p$ to $V$ at any instant is constant and equals to 1 . What is the molar heat capacity of the gas?

(2006, 3M)

(a) $\frac{4 R}{2}$

(b) $\frac{3 R}{2}$

(d) 0

Show Answer

Solution:

Given, $\frac{p}{V} = 1 \Rightarrow p = V$

Also from first law : $d q = C_{V} d T + p d V$

For one mole of an ideal gas : $p V = R T$

$\begin{array}{lrl} \Rightarrow & p d V + V d p & = R d T From (i) & p d V & = V d p \end{array}$

Substituting in Eq. (ii) gives

$\begin{aligned} 2 p d V & = R d T \Rightarrow p d V = \frac{R}{2} d T \Rightarrow & d q & = C_{V} d T + \frac{R}{2} d T \Rightarrow & \int \frac{d q}{d T} & = C_{V} + \frac{R}{2} = \frac{3}{2} R + \frac{R}{2} = 2 R \end{aligned}$

Thermodynamics and Thermochemistry 1 Question 27

30. A monoatomic ideal gas undergoes a process in which the ratio of $p$ to $V$ at any instant is constant and equals to 1 . What is the molar heat capacity of the gas?

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

Thermodynamics and Thermochemistry 1 Question 27

30. A monoatomic ideal gas undergoes a process in which the ratio of p to V at any instant is constant and equals to 1 . What is the molar heat capacity of the gas?

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

Menu

30. A monoatomic ideal gas undergoes a process in which the ratio of $p$ to $V$ at any instant is constant and equals to 1 . What is the molar heat capacity of the gas?