Question:
A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume of this process is $TV^x = \text{constant}$. Then $x$ is
A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume of this process is $TV^x = \text{constant}$. Then $x$ is
Show Hint
For a monoatomic gas ($f=3$), $x = 2/3$. For a diatomic gas ($f=5$), $x = 2/5$. The value of $x$ is simply $2/f$. Memorizing this ratio saves time!
Updated On: Jul 1, 2026
- $\frac{5}{3}$
- $\frac{2}{5}$
- $\frac{2}{3}$
- $\frac{3}{5}$
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
In an adiabatic process, the relationship between temperature and volume is governed by the adiabatic index ($\gamma$).
1. The Adiabatic Relation:
The standard equation is $TV^{\gamma-1} = \text{constant}$.
Comparing this to the given $TV^x = \text{constant}$, we find:
$$x = \gamma - 1$$
2. Determine $\gamma$ for Diatomic Gas: For a rigid diatomic gas (at room temperature, vibrational modes are not active): The degrees of freedom $f = 5$ (3 translational + 2 rotational). $$\gamma = 1 + \frac{2}{f} = 1 + \frac{2}{5} = \frac{7}{5}\lt strong\gt 3. Calculate $x$:\lt /strong\gt x = \gamma - 1$$ $$x = \frac{7}{5} - 1 = \frac{2}{5}$$ Therefore, the value of $x$ is $2/5$.
2. Determine $\gamma$ for Diatomic Gas: For a rigid diatomic gas (at room temperature, vibrational modes are not active): The degrees of freedom $f = 5$ (3 translational + 2 rotational). $$\gamma = 1 + \frac{2}{f} = 1 + \frac{2}{5} = \frac{7}{5}\lt strong\gt 3. Calculate $x$:\lt /strong\gt x = \gamma - 1$$ $$x = \frac{7}{5} - 1 = \frac{2}{5}$$ Therefore, the value of $x$ is $2/5$.
Was this answer helpful?
0
0
Top AP ECET ME Physics Questions
- If the unit of mass is $1\text{ kg}$, the unit of length is $1\text{ m}$ and the unit of time is $1\text{ minute}$, the unit of pressure in $\text{Nm}^{-2}$ is
- $MLT^{-1}$ is the dimensional formula for
- If $|\vec{A} \times \vec{B}| = \sqrt{3} \vec{A} \cdot \vec{B}$ then the value of $|\vec{A} + \vec{B}|$ is
- Of the vectors given below, the parallel vectors are $\vec{A} = 6\hat{i} + 8\hat{j}$, $\vec{B} = 210\hat{i} + 280\hat{k}$, $\vec{C} = 5.1\hat{i} + 6.8\hat{j}$, $\vec{D} = 3.6\hat{i} + 8\hat{j} + 48\hat{k}$
- The position $x$ of a particle with respect to time '$t$' along x- axis is given by $x = 9t^2 - t^3$ where $x$ is in metres and $t$ in seconds. The position of this particle when it achieves maximum speed along the x direction is
View More Questions
Top AP ECET ME Thermodynamics Questions
- If the pressure of an ideal gas contained in a closed vessel is increased by $0.5\%$, the increase in temperature is $2^\circ\text{C}$. The initial temperature of the gas is
- During the free expansion of an ideal gas, which of the following physical quantity remains constant
- The specific heat at constant volume for a monoatomic gas is $0.075\text{ cal/kg}\cdot\text{K}$ and its gram molecular specific heat is $3\text{ cal/mol}\cdot\text{K}$. Then mass of one atom of that gas is
- A carnot engine having an efficiency of $\frac{1}{10}$ as heat engine, is used as a refrigerator. If the work done on the system is $10 \text{ J}$, the amount of energy absorbed from the reservoir at lower temperature is
Top AP ECET ME Questions
- Order of the matrix $\begin{bmatrix} 1 & 6 \\ 2 & 0 \\ 7 & -1 \end{bmatrix}$ is
- If two rows (or columns) of a determinant of order 3 are identical then the value of determinant is
- Co-factor of -4 in $\begin{vmatrix} 1 & 2 & 3 \\ -4 & 3 & 6 \\ 2 & -7 & 9 \end{vmatrix}$ is
- The Matrix $\begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix}$ is
- If $A = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix}$ then $(A^{-1}) =$
View More Questions