Thermal Properties of Matter Test

Result

Thermal Properties of Matter Test - 54

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

One mole of an ideal gas expands against a constant external pressure of 1 atm from a volume of $$10d{ m }^{ 3 }$$ to a volume of $$30d{ m }^{ 3 }$$. What would be the work done in joules?

A
$$-2026 J$$

B
$$+2026 J$$

C
$$-1947 J$$

D
$$1648 J$$

Solution

$$\begin{array}{l} Work\, done\, for\, isothermal\, ansion,W=-\int _{ { V_{ 1 } } }^{ { V_{ 2 } } }{ pdV } \\ { { Sin } }ce,\, \rho \, is\, cons\tan t, \\ W=-\int _{ { V_{ 1 } } }^{ { V_{ 2 } } }{ dV } \\ W=-\rho \left( { { V_{ 2 } }-{ V_{ 1 } } } \right) \\ W=-1\, atm\left( { 30-10 } \right) L \\ =-20\, atm\, L \\ Now,\, 0.08206\, L\, atm=8.314J\left( { As\, we\, know } \right) \\ -20\, atm\, L=\dfrac { { 8.314 } }{ { 0.08206 } } \times -20J \\ =-2026.32J \end{array}$$
Hence,
option $$(A)$$ is correct answer.
Question 2
1 / -0

Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from $${ 20 }^{ 0 }C$$ to $${ 90 }^{ 0 }C$$ . Work done by gas is close to : ( gas constant R=8.31 j / mol -k )

A
146 j

B
581 j

C
73 j

D
291 j

Solution
Question 3
1 / -0

Coefficient of real expansion mercury is $$0.18 \times {10^{ - 3}}{/^0}C.$$ if the density of mercury at $${0^0}C$$ is $$13.6 gm/C.C,$$ then is density at $$473K$$ will be$$:$$

A
$$13.11 \%$$

B
$$3.6 \%$$

C
$$36 \%$$

D
$$24.4 \%$$

Solution

Coefficient of real expansion of mercury, $$r_0=0.18\times 10^{-3}\,/^0C$$

Initial temperature $$0^0C=273\,K$$

Density of mercury $$13.6\,gm/c^3$$

Final temperature $$473\,K$$

We need to calculate the density at $$473\,K$$ or $$200^0C$$

We have,

$$\rho=\dfrac{\rho_0}{1+r_0 T}$$

where,

$$\rho_0=$$ Density at $$0^0C$$

$$r_0=$$ Coefficient of volume expansion

$$T=$$ Temperature at which density is to be calculated

Putting the values in the formula,

$$\rho=\dfrac{13.6}{1+0.18\times 200}$$

$$=\dfrac{13.6}{1.036}=13.11\,g/cc$$
Question 4
1 / -0

An ideal gas at pressure P is adiabatically compressed so that its density becomes n times the initial value. The final pressure of the gas will be $$ ( \gamma= C_p/C_v) $$

A
$$ n^\gamma P $$

B
$$ n^{-\gamma} P $$

C
$$ n^{\gamma-1} P $$

D
$$ n^{1-\gamma} P $$

Solution
Question 5
1 / -0

N moles of a monoatomic gas is carried round the reversible rectangular cycle ABCDA as shown in the diagram. The temperature at $$A$$ is $$T _ { 0 }$$ . The thermodynamic efficiency of the cycle is

A
$$ 15 \%$$

B
$$ 50 \%$$

C
$$ 20 \%$$

D
$$ 25 \%$$

Solution

$$\begin{array}{l} At\, \, A\, \, { P_{ 0 } }{ V_{ 0 } }=nR{ T_{ 0 } }\to \left( i \right) \\ At\, \, B\, \, 2{ P_{ 0 } }{ V_{ 0 } }=nR{ T_{ 1 } }\to \left( { ii } \right) \end{array}$$
Efficiency of thermodynamic cycle
$$\eta = 1 - \frac{{{T_B}}}{{{T_A}}}$$
$$By\left( i \right)\,\,and\,\,\left( {ii} \right)$$
$$\dfrac{{{T_B}}}{{{T_A}}} = \dfrac{1}{2}$$
$$\eta = 1 - \frac{1}{2} = \dfrac{1}{2} = 50\,\,\% $$
Option B.
Question 6
1 / -0

Rate of emission thermal radiation of a spherical black body of radius $$r$$ is $$H$$. It rate of cooling is $$C$$. Then

A
$$H\propto \,r$$

B
$$H\propto \,{r^3}$$

C
$$C\,\propto\,\dfrac{1}{r}$$

D
$$C\,\propto \,\dfrac{1}{{{r^2}}}$$

Solution

According to Stefan's law,
$$H=\sigma eAT^4= \sigma e (4\pi r^2)T^4$$. . . . . . .(1)
$$H\propto r^2$$
$$\sigma e AT^4=ms\dfrac{dT}{dt}$$

$$\dfrac{dT}{dt}=C=\dfrac{\sigma e A T^4}{ms}$$

$$C=\dfrac{\sigma e T^4(4\pi r^2)}{(\rho \dfrac{4}{3}\pi r^3)s}$$ ($$m=\rho \dfrac{4}{3}\pi r^3$$)

$$C\propto \dfrac{1}{r}$$

The correct option is C.
Question 7
1 / -0

The volume of an ideal gas is 1 litre and its pressure is equal to 72 cm of mercury column. The volume of gas is made $$ 900 cm^3 $$ by compressing it isothermally. The stress of the gas will be

A
8 cm (mercury)

B
7 cm (mercury)

C
6 cm (mercury)

D
4 cm (mercury)

Solution
Question 8
1 / -0

A device in which the loss of heat due to conduction, convection and radiation is minimized is

A
Solar cell

B
Solar cooker

C
Thermometer

D
Thermos flask

Solution
Question 9
1 / -0

In which of the following processes, convection does not take place primarily?

A
Sea and land breeze

B
Boiling of water

C
Heating air around a furnace

D
Warming of glass of bulb due to filament

Solution

Warming of glass of bulb is due to the radiation coming from hot filament of bulb not due to convection.
The remaining three options A , B and C are results of convection.
A
The air above the land warms up and rises and the cool air over the sea moves in to take its place, resulting in the sea breeze in the daytime. At night, as the sea maintains its temperature better and is warmer than the land, the roles of land and sea reverse and convection of air results in the land breeze.
B
When boiling water, the temperature of molecules within the water increases and they slowly begin to move at a rapid rate, upwards. These molecules produce kinetic energy. The hot water molecules become less dense, and they rise above the denser cooler molecules. This movement of molecules creates convection currents. Boiling water is an example of forced convection.
C
A furnace is very hot from inside.The air from around the furnace gets heated and expands and rises above and cooler air from surroundings take this place.And this processes goes on and on .Hence this is also a result of convection.
Question 10
1 / -0

An isotropic point source having radiation power P is located on the axis of an ideal circular mirror of radius r .The distance between the source and the plate is l which is much bigger than radius of the plate .Force that the light exerts on the plate is

A
$$\cfrac{P}{2c}\left[\cfrac{r^{2}}{l^{2}}\right]$$

B
$$\cfrac{2P}{c}\left[\cfrac{r^{2}}{l^{2}}\right]$$

C
$$\cfrac{P}{c}\left[\cfrac{r^{2}}{l^{2}}\right]$$

D
$$\cfrac{P}{4c}\left[\cfrac{r^{2}}{l^{2}}\right]$$