The bulk modulus of a gas is defined as $B=-V d p / d V$. For an adiabatic process the variation of $B$ is proportional to $p^n$. For an ideal gas $n$ is
KVPY 2013, Medium
Download our app for free and get started
(b)
Adiabatic bulk modulus for an ideal gas is
$\quad K=\frac{d p}{-d V / V}=-V\left(\frac{d p}{d V}\right)$
$\quad=\gamma P \quad \dots(i)$
Now given,
$\quad K \propto p^n \quad \dots(ii)$
$\therefore$ From Eqs. $(i)$ and $(ii)$, we have
$\Rightarrow \quad n=1$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A wire suspended vertically from one end is stretched by attaching a weight $200 \,N$ to the lower end. The weight stretches the wire by $1 \,mm$. The elastic potential energy gained by the wire is ....... $J$View Solution
- 2The value of force constant between the applied elastic force $F$ and displacement will beView Solution
- 3The ratio of radii of two wires of same material is $2: 1$. If these wires are stretched by equal force, the ratio of stresses produced in them is .............View Solution
- 4A uniform cubical block is subjected to volumetric compression, which decreases its each side by $2 \%$. The Bulk strain produced in it is ............View Solution
- 5A wire suspended vertically from one of its ends is stretched by attaching a weight of $200\, N$ to the lower end. The weight stretches the wire by $1\, mm$ Then the elastic energy stored in the wire is ........ $J$View Solution
- 6The interatomic distance for a metal is $3 \times {10^{ - 10}}\,m$. If the interatomic force constant is $3.6 \times {10^{ - 9}}\,N/{{\buildrel _{\circ} \over {\mathrm{A}}}}$, then the Young's modulus in $N/{m^2}$ will beView Solution
- 7Two steel wires of same length but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown. The force stretches the combination by $10\ mm$. How far does the midpoint $A$ move ............ $mm$View Solution
- 8Two wires of copper having the length in the ratio $4 : 1$ and their radii ratio as $1 : 4$ are stretched by the same force. The ratio of longitudinal strain in the two will beView Solution
- 9Which one of the following is the Young’s modulus $($in $N/m^2)$ for the wire having the stress-strain curve shown in the figureView Solution
- 10Young's modules of material of a wire of length ' $L$ ' and cross-sectional area $A$ is $Y$. If the length of the wire is doubled and cross-sectional area is halved then Young's $modules$ will be :View Solution