Thermodynamics

U = aP?
PV/ (γ-1) = aP?
P? ³V = a (γ - 1)
PV? ¹? ³ = constant
Comparing with PV? = constant
x = -?
C = R/ (γ-1) + R/ (1-x) = R/ (5/3 - 1) + R/ (1 +? ) = 3R/2 + 3R/4
C = 9R/4

According to Newton's law of cooling
(T? -T? )/t = K [ (T? +T? )/2 - T? ]
For 1? cup of coffee,
(90-80)/t = K [ (90+80)/2 - 20]
For 2? cup of coffee,
(80-60)/t' = K [ (80+60)/2 - 20]
Divide (1) by (2)
t'/t = 65/50 ⇒ t' = (13/5)t

Bromobenzene is formed in first step (Sandmeyer reaction), which further gives phenyl magnesium bromide. Phenyl magnesium bromide further gives benzene with water.

+Mg (Br)OH

BeCl? in solid state exist in a polymeric form & in a vapour state in exist in a dimeric form.

chain polymeric structure
Vapour state exist in a dimeric form

Maximum work is done in the case where area under the curve is maximum.

$\mathrm{T}\mathrm{i}=-{50}^{?}\mathrm{C}$

$\begin{array}{rr}& =223\mathrm{K}\\ & {\mathrm{V}}_{\mathrm{r}\mathrm{m}\mathrm{s}}\propto \sqrt[]{\mathrm{T}}\end{array}$

As ${\mathrm{v}}_{\mathrm{r}\mathrm{m}\mathrm{s}}$  increased by 3 times

So ${\left({\mathrm{v}}_{\mathrm{r}\mathrm{m}\mathrm{s}}\right)}_{\mathrm{f}}=4{\left({\mathrm{v}}_{\mathrm{r}\mathrm{m}\mathrm{s}}\right)}_{\text{initial}}$

${\mathrm{T}}_{\mathrm{f}}=16{\mathrm{T}}_{\mathrm{i}}$

$=16*223$

$=3568\mathrm{K}$ ${\mathrm{T}}_{\mathrm{f}}=(3568-273{)}^{?}\mathrm{C}$

$={3295}^{?}\mathrm{C}$

15. (c) Fundamental harmonic frequency open pipe

$=\frac{\mathrm{V}}{2\mathrm{L}}={\mathrm{v}}_1$

(say)

Fundamental harmonic frequency of closed pipe $=\frac{\mathrm{V}}{4\mathrm{L}}$

$={\mathrm{v}}_2$ (say)

$\Rightarrow \frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}=\frac{\frac{\mathrm{V}}{2\mathrm{L}}}{\frac{\mathrm{V}}{4\mathrm{L}}}\mathrm{}2:1$

Kindly go through the answers

S? * S?

PV? = C ⇒ V? (dP/dV) + P (γV^ (γ-1) = 0 ⇒ dP/dV = -γ (P/V) ⇒ dP/P = -γ (dV/V)

Pressure decreases with an increase in volume in both isothermal and adiabatic processes. In an adiabatic process, as volume decreases, pressure increases with the increase in temperature.

In an LCR series AC circuit, the phase difference φ between current and voltage is: φ = tan? ¹ (X? - X? ) / R)

If each vibrational mode contributes two degrees of freedom and the total degrees of freedom f = 3 + 3 + 4 = 10, then:
β = 1 + 2/f = 1 + 2/10 = 1.2