Thermal Properties of Matter Test

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Thermal Properties of Matter Test - 44

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Weekly Quiz Competition

Question 1
1 / -0

The thermal conductivity of a material in CGS system is 0.4. In steady state the rate of flow of heat $$10 \,cal/s-cm^2$$, then the thermal gradient will be

A
$$15^o C/cm$$

B
$$25^o C/cm$$

C
$$50^o C/cm$$

D
$$75^o C/cm$$

Solution

$$\dfrac{\Delta Q}{\Delta t}=\dfrac{KA\Delta T}{\Delta x}$$
Thermal gradient $$\dfrac{\Delta T}{\Delta x}$$ is given by
$$\dfrac{\left ( \dfrac{\Delta Q}{\Delta t} \right )}{KA}=\dfrac {10}{0.4}= 25^o C/ cm$$
Question 2
1 / -0

A building at a temperature T(in k) is heated by an ideal heat pump which uses the amosphere at $$T_0(k)$$. What is the equilibrium temperature of the building ?

A
$$T_o+\dfrac{W}{2\alpha}+ \sqrt{T_0\dfrac{W}{\alpha}+(\dfrac{W}{2\alpha})^2}$$

B
$$T_0-\dfrac{W}{2\alpha}_\sqrt{T_0\dfrac{W}{2\alpha}+(\dfrac{W}{2\alpha})^2}$$

C
$$T_o+\dfrac{W}{2\alpha}- \sqrt{T_0\dfrac{W}{\alpha}+(\dfrac{W}{2\alpha})^2}$$

D
$$T_0-\dfrac{W}{2\alpha}_\sqrt{T_0\dfrac{W}{2\alpha}+(\dfrac{W}{\alpha})^2}$$
Question 3
1 / -0

Two metal rods, rod-1 and rod-2 of equal length are welded together end to end.Under steady state conditions, when the free end of the end of the rod-1 is kept at $$100^0C$$ and the free end of the rod -2 is kept at $$0^0C$$ , the temperature at the welded junction is approximately.
[Thermal conductivity of rod-1 = $$92 J s^{-1}m^{-1}K^{-1}$$, and rod-2 =$$16 J s^{-1}m^{-1}K^{-1}$$]

A
$$85^0C$$

B
$$50^0C$$

C
$$75^0C$$

D
$$95^0C$$

Solution

Heat Current = $$i = \dfrac{KA \Delta T}{L}$$
$$K_1(T_1-T) = K_2(T-T_2)$$
$$92(100-T)=16(T-0)$$
$$\implies T = 85^o C$$
Question 4
1 / -0

The radii of two spheres made of same metal are $$r$$ and $$2r$$. These are heated to the same temperature and placed in the same surrounding. The ratio of rates of decrease of their temperature will be:

A
$$1 : 1$$

B
$$4 : 1$$

C
$$1 : 4$$

D
$$2 : 1$$

Solution

Same metal $$\implies$$ same density
Rate of cooling
$$\dfrac { -dT }{ dt } =\dfrac { eA\sigma }{ mc } \left( { T }^{ 4 }-{ T }_{ 0 }^{ 4 } \right) $$ formula used.
T is same for both spheres
$${ T }_{ 0 }$$ is same
L is same
$$\sigma $$
e is same
Here rate of cooling proportional $$\propto \dfrac { A }{ m } $$
$$\propto \dfrac { 4{ \pi r }^{ 2 } }{ D\times 4{ \pi r }^{ 3 } } $$
Density $$\propto\dfrac { 1 }{ Dr } $$, D=Density =Mass/volume
$${ R }_{ 1 }$$ = rate of cooling of radius $${ r }_{ 1 }$$
$${ R }_{ 2 }$$ = rate of cooling of radius $${ r }_{ 2 }$$
$$\dfrac { { R }_{ 1 } }{ { R }_{ 2 } } =\dfrac { { D }_{ 2 }{ \quad r }_{ 2 } }{ { D }_{ 1 }\quad { r }_{ 2 } } \quad \left[ { D }_{ 1 }={ D }_{ 2 }\quad same\quad density \right] $$
$$=2:1$$
Question 5
1 / -0

'Thermos Flask' was invented by

A
Dewar

B
daimler

C
Urey

D
None of these

Solution
Question 6
1 / -0

Thermal radiation can be detected by.

A
A thermometer

B
A radiometer

C
A bolometer

D
All of the above

Solution

Thermal radiation can be detected by thermometer, radiometer, bolometer.
Question 7
1 / -0

Which one of the following statements is not true regarding thermal radiations?

A
All bodies emit thermal radiation at all temperatures

B
They are electromagnetic in nature

C
They travel in straight line with a velocity of $$3\times 10^8$$ m/s in free space

D
They cannot be reflected by mirrors

Solution

All bodies emit thermal radiation at all temperatures.They are electromagnetic in nature and have same speed. But they cannot be reflected by mirror as thermal energy is not visible.
Question 8
1 / -0

A cube, a thin circular plate, and a sphere are made of the same metal and having the same mass and same volume. They are initially heated to the same temperature. When left in air at the room temperature, which of these bodies will cool fastest and slowest respectively?

A
The cube; the sphere

B
The circular plate; the cube

C
The circular plate; the sphere

D
The sphere; the circular plate

Solution

For a given volume, among all the three objects, the sphere has the least surface area and the cube will have the maximum surface area. This is also due to the fact that the volume and mass of all three are the same.

According to Heat theory, the rate of loss of heat is proportional to the surface area of the object. Hence, the rate of cooling will be slowest for the sphere and fastest for the cube.

Thus the correct option is A.
Question 9
1 / -0

The temperature (T) of one mole of an ideal gas varies with its volume (V) as $$T = -\alpha { V }^{ 3 }+\ \beta { V }^{ 2 }$$, where $$\alpha$$ and $$\beta$$ are positive constants. The maximum pressure of gas during this process is

A
$$\dfrac { \alpha \beta }{ 2R } $$

B
$$\dfrac { { \beta }^{ 2 }R }{ 4\alpha }$$

C
$$\dfrac { (\alpha +\beta )R }{ { 2\beta }^{ 2 } }$$

D
$$\dfrac { { \alpha }^{ 2 }R }{ { 2\beta } }$$

Solution

$$T=-\alpha V^3+\beta V^2\\ \cfrac{PV}{R}=-\alpha V^2+\beta V^2\\ P=RV(-\alpha V+\beta)$$

For maximum pressure

$$\cfrac{dP}{dV}=0\\ \Rightarrow -2\alpha V+\beta =0\\ \Rightarrow V=\cfrac{\beta }{2\alpha}\\ P=R[-\alpha(\cfrac{\beta }{2\alpha})^2+\cfrac{\beta }{2\alpha}\times \beta]\\P=R[\cfrac{-\beta^2}{4\alpha}+\cfrac{\beta^2}{2\alpha}]\\P=\cfrac{R\beta^2}{4\alpha}$$
Question 10
1 / -0

Two identical glass bulbs are interconnected by a thin glass tube at $$0^{\circ}C$$. A gas is filled at N.T.P. in these bulb is placed in ice and another bulb is placed in hot bath, then the pressure of the gas becomes $$1.5\ times$$. The temperature of hot bath will be

A
$$100^{\circ}$$

B
$$182^{\circ}C$$

C
$$256^{\circ}C$$

D
$$546^{\circ}C$$

Solution

Quantity of gas in these bulbs is constant i.e,
Initial no. of moles in both bulb $$=$$ final no. of moles
$$\Rightarrow n_1+n_2={ n }_{ 1 }^{ ' }+{ n }_{ 2 }^{ ' }$$
$$\Rightarrow \dfrac{PV}{R(273)}+\dfrac{PV}{R(273)}=\dfrac{1.5PV}{R(273)}+\dfrac{1.5PV}{R(T)}$$
$$\Rightarrow \dfrac{2}{273}=\dfrac{1.5}{273}+\dfrac{1.5}{T}$$
$$\Rightarrow T=819K$$
$$=546°C$$
Hence, the answer is $$546°C.$$

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Re-Attempt Weekly Quiz Competition

Thermal Properties of Matter Test - 44

Result

Thermal Properties of Matter Test - 44

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SHARING IS CARING

Question 1

$$15^o C/cm$$

$$25^o C/cm$$

$$50^o C/cm$$

$$75^o C/cm$$

Solution

Question 2

$$T_o+\dfrac{W}{2\alpha}+ \sqrt{T_0\dfrac{W}{\alpha}+(\dfrac{W}{2\alpha})^2}$$

$$T_0-\dfrac{W}{2\alpha}_\sqrt{T_0\dfrac{W}{2\alpha}+(\dfrac{W}{2\alpha})^2}$$

$$T_o+\dfrac{W}{2\alpha}- \sqrt{T_0\dfrac{W}{\alpha}+(\dfrac{W}{2\alpha})^2}$$

$$T_0-\dfrac{W}{2\alpha}_\sqrt{T_0\dfrac{W}{2\alpha}+(\dfrac{W}{\alpha})^2}$$

Question 3

$$85^0C$$

$$50^0C$$

$$75^0C$$

$$95^0C$$

Solution

Question 4

$$1 : 1$$

$$4 : 1$$

$$1 : 4$$

$$2 : 1$$

Solution

Question 5

Dewar

daimler

Urey

None of these

Solution

Question 6

A thermometer

A radiometer

A bolometer

All of the above

Solution

Question 7

All bodies emit thermal radiation at all temperatures

They are electromagnetic in nature

They travel in straight line with a velocity of $$3\times 10^8$$ m/s in free space

They cannot be reflected by mirrors

Solution

Question 8

The cube; the sphere

The circular plate; the cube

The circular plate; the sphere

The sphere; the circular plate

Solution

Question 9

$$\dfrac { \alpha \beta }{ 2R } $$

$$\dfrac { { \beta }^{ 2 }R }{ 4\alpha }$$

$$\dfrac { (\alpha +\beta )R }{ { 2\beta }^{ 2 } }$$

$$\dfrac { { \alpha }^{ 2 }R }{ { 2\beta } }$$

Solution

Question 10

$$100^{\circ}$$

$$182^{\circ}C$$

$$256^{\circ}C$$

$$546^{\circ}C$$

Solution

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