physics ncert solutions class 11th

Soap bubble radius, r = 5.0 mm = 5 $*{10}^{-3}$ m

Surface tension of the soap bubble, S = 2.50 $*{10}^{-2}$ N/m

Relative density of soap solution = 1.20, hence density of soap solution,  $?$ = 1.2 $*{10}^3$ Kg/ $m^3$

Air bubble formed at a depth, h = 40 cm = 0.4 m

1 atmospheric pressure = 1.01 $*{10}^5$ Pa

Acceleration due to gravity, g = 9.8 m/ $s^2$

We know, the excess pressure inside the soap bubble is given by the relation:

P = $\frac{4S}{r}$ = $\frac{4*2.50*{10}^{-2}}{5*{10}^{-3}}$ Pa = 20 Pa

Hence, the excess pressure inside the air bubble is given by the relation, P' = $\frac{2S}{r}$ = 10 Pa

At a depth of h, the total pressure inside the air bubble = Atmospheric pressure + h $?$ g +P'

= 1.01 $*{10}^5$ + (0.4 $*1.2*{10}^3*9.8)$ + 10 Pa = 105714 Pa = 1.06 $*{10}^5$ Pa

11.21 

(a) The P-T phase diagram for CO₂ is shown here. O is the triple point of the CO₂ phase diagram. This means that at the temperature and pressure corresponding to this point, the solid, liquid and vaporous phases of CO₂ exists in equilibrium.

(b) The fusion and the boiling points of CO₂ decreases with a decrease in pressure.

(c) The critical temperature and critical pressure of CO₂ are 31 $?$ 72.9 atm respectively. Even if it is compressed to a pressure greater than 72.9 atm, CO₂ will not liquefy above the critical temperature.

(d) It can be concluded from the P-T phase diagram of CO2 that:

CO₂ is gaseous at -70 $?$, under 1 atm pressure.

CO₂ is solid at -60 $?$ , under 10 atm pressure.

CO2 is liquid at 15 $?$ , under 56 atm pressure.

Speed of the wind on the upper surface of the wing, $V_1$ = 70 m/s

Speed of the wind on the lower surface of the wing, $V_2$ = 63 m/s

Area of the wing, A = 2.5 $m^2$

Density of air, $\rho$ = 1.3 kg/ $m^3$

According to Bernoulli's theorem, we have the relation:

$P_1$ + $\frac{1}{2}\rho {V_1}^2$ = $P_2$ + $\frac{1}{2}\rho {V_2}^2$

( $P_2$ - $P_1$ )= $\frac{1}{2}\rho ({V_1}^2$ - ${V_2}^2)$ , where $P_1$ = pressure on the upper surface of the wing and $P_2$ - pressure on the lower surface of the wing

The pressure difference provides lift to the aeroplane

Lift on the wing = ( $P_2$ - $P_1$ )A = $\frac{1}{2}\rho ({V_1}^2$ - ${V_2}^2)$ A = $\frac{1}{2}*1.3*({70}^2$ - ${63}^2)*2.5$ N = 1512.8 N = 1.5 $*{10}^3$ N

11.19 (a) A body with a large reflectivity is a bad absorber. A bad absorber will in turn be a poor emitter of radiations.

(b) Brass is a good conductor of heat, when one touches a brass tumbler, heat is conducted from the body to the brass tumbler easily. Hence, the temperature of the body reduces to a colder value and one feels cold.

On the other hand, wood is a poor conductor of heat. Very little heat is conducted from the body to the wooden tray. Resulting in negligible drop in body temperature.

Thus a brass tumbler feels colder than a wooden tray on a chilly day.

(c) Black body radiation equation is given by:

E = $\sigma$ ( $T^4$ - $T_o^4$ ), where

E = energy radiation

$\sigma$ = constant

$T=$ temperature of the optical pyrometer

$T_o$ = Temperature of open space

$\mathrm{H}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{}\mathrm{}\mathrm{a}\mathrm{n}\mathrm{}\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{}\mathrm{i}\mathrm{n}\mathrm{}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{}\mathrm{s}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{e}\mathrm{}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}$

When the same piece of iron placed in a furnace, the radiation energy is E = $\sigma T^4$

(d) In the absence of atmospheric gases, no extra heat will be trapped. All the heat would be radiated back from Earth's surface.

(e) A heating system based on the circulation of steam is more efficient in warming a building than that based on the circulation of hot water. This is because steam contains surplus heat in the form of latent heat ( 540 cal/g)