Class 11th

In adiabatic process
PV? = constant
P (m/ρ)? = constant
As mass is constant
P ∝ ρ?
P_f/P_i = (ρ_f/ρ_i)? = (32)? /? = 2? = 128

Aq. $\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}$  in a burette and aqueous oxalic acid in a conical flask.

At T°C L = L? + L?
At T +? T Leq = L'? + L'?
where L'? = L? (1 + α? T)
L'? = L? (1 + α? T)
Leq = (L? + L? ) (1 + αavg? T)

⇒ (L? + L? ) (1 + αavg? T) = L? + L? + L? α? T + L? α? T
⇒ (L? + L? )αavg = L? α? + L? α?
⇒ αavg = (L? α? + L? α? )/ (L? + L? )

Isohexane and 3-Methylpentane having same molecular formula. Isohexane boil at ${60}^{?}\mathrm{C}$ and 3-Methyul pentane boils at ${63}^{?}\mathrm{C}$ . Both having low boiling point difference so fractional distillation is useful for separation and isohexane having low boiling point so comes out first.

Ethyl acetate $\left(\begin{array}{c}{\mathrm{C}\mathrm{H}}_3-\mathrm{C}-{\mathrm{O}\mathrm{C}}_2{\mathrm{H}}_5\\ ?\\ \mathrm{O}\end{array}\right)$  is polar molecule, so dipole-dipole and London

Forces will be present between them.

Initially S? L = 2m
S? L = √2² + (3/2)²
S? L = 5/2 = 2.5 m
? x = S? L - S? L = 0.5 m
So since λ = 1 m. ∴? x = λ/2
So white listener moves away from S? Then? x (= S? L − S? L) increases and hence, at? x = λ first maxima will appear.? x = λ = S? L − S? L.
1 = d - 2 ⇒ d = 3 m.

$\mathrm{}{f}^{\mathrm{\text{'}}}\left(x\right)=a(x+1)(x-1)x^2$

$f^{\mathrm{\text{'}}}\left(x\right)=a{x}^4-x^{2}f$

$f\left(x\right)=\frac{a{x}^5}{5}-\frac{a{x}^3}{5}+C$
$?f\left(0\right)=0\Rightarrow c=0$

${\mathrm{l}\mathrm{i}\mathrm{m}}_{x\to 0}?\frac{f\left(x\right)}{x^3}=2$

$\Rightarrow \mathrm{a}=-6$

Minima at $\therefore f^{\mathrm{\text{'}}}\left(x\right)=-6\left(x^2-1\right)\left(x^2\right)$

Maxima at $x=-1$

Gypsum $\stackrel{393\mathrm{K}}{?}{\mathrm{C}\mathrm{a}\mathrm{S}\mathrm{O}}_4\frac{1}{2}{\mathrm{H}}_2\mathrm{O}$