Thermal Properties of Matter Test

Result

Thermal Properties of Matter Test - 66

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Question 1
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Two rods A and B of same length and radius are joined together. the thermal conductivity of A and B are $$2K$$ and $$K$$. Under steady state conditions, if the temperature difference between the open ends of A and B is $$36^{\circ}C$$, the temperature difference across 'A' is:

A
$$12^{\circ}C$$

B
$$18^{\circ}C$$

C
$$24^{\circ}C$$

D
$$9^{\circ}C$$

Solution
Question 2
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If the temperature of a hot body is increased by 50% then the increase in the quantity of emitted heat radiation will be

A
125%

B
200%

C
300%

D
400%

Solution

let us assume initial Temperature $$T_1=T$$ then final will be

$$T_2=\dfrac{50}{100}T+T=\dfrac{150}{100}T=\dfrac{15}{10}T$$

energy radiated

$$e_1=\sigma A T_1^4\quad \left(1\right)$$

$$e_2=\sigma A T_2^4\quad \left(2\right)$$

$$\%$$ increase in radiation

$$=\dfrac{e_2-e_1}{e_1}\times 100$$

$$=\dfrac{\sigma A T_2^4-\sigma A T_1^4}{\sigma A T_1^4}\times 100$$

$$\dfrac{\left(\dfrac{15}{10}T\right)^4-T^4}{T^4}\times 100$$

$$\dfrac{15^4-10^4}{10^4}\times 10^2$$

$$\dfrac{50625-10000}{10^2}$$

$$=406.25$$

$$\approx 400\%$$
Hence $$(d)$$ option is correct.
Question 3
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A copper block A of mass 500 gm and $$S_p$$ heat 0.1 cal/gm/$$ ^ { \circ } C$$ is heated from $$30 ^ { \circ } C \text { to } 40 ^ { \circ } C$$. Another identical copper block B of same mass is heated from $$35 ^ { \circ } C \text { to } 40 ^ { \circ } C$$. The ratio of their thermal capacities is:

A
1 : 2

B
2 : 1

C
1 : 1

D
1 : 4

Solution
Question 4
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Two identical square rods of metal are welded end to end as shown in figure (a). $$20$$ calories of heat flows through it in $$4$$ minutes. if the rods are welded as shown in figure (b), the same amount of heat will flow through the rods in

A
$$1$$ minute

B
$$2$$ minutes

C
$$4$$ minutes

D
$$16$$ minutes

Solution

The rate at which the heat is developed is given by
$$\dfrac{dQ}{dt} = \dfrac{KA \delta T }{L}$$
$$\dfrac{dQ}{dt} = \dfrac{KA \delta (T_1-T_2) }{2x}$$
=5
Now , we have $$\dfrac{dQ}{dt} = \dfrac{2 KA \delta T }{x}$$
Therefore by solving above we have , t=2 minutes
Question 5
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In a container of negligible heat capacity $$100 gm$$ of a liquid at $$20 ^ { \circ } \mathrm { C }$$ is heated. Specific heat of the liquid varies with temperature given as $$s = ( 100 T + 500 ) J / k g ^ { \circ } C$$ where $$T$$ is in$$^{ \circ }C$$ . Find the amount of heat required to raise the temperature of the liquid to $$40 ^ { \circ } \mathrm { C }$$

A
$$5000 J$$

B
$$6000 J$$

C
$$7000 J$$

D
$$8000 J$$

Solution
Question 6
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A copper bar $$10\ cm$$ long has its ends passed against copper tanks at $$0^{o}C$$ and $$100^{o}C$$. The ends are separated by layers of dust $$0.1\ mm$$ thick. If conductivity of dust is $$0.001$$ times that of copper, the temperature of end $$P$$ and $$Q$$ of bar are [Take rate of flow of heat constant from $$P$$ to $$Q$$]

A
$$33.3^{o}C$$ and $$66.7^{o}C$$

B
$$66.7^{o}C$$ and $$33.3^{o}C$$

C
$$75^{o}C$$ and $$25^{o}C$$

D
$$60^{o}C$$ and $$40^{o}C$$
Question 7
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The pressure of the gas contained in a closed vessel is increased by $$0.4\%$$ when heated by $$1^oC$$. The initial temperature of the gas must be

A
$$1250 K$$

B
$$250 K$$

C
$$2500 K$$

D
$$25^oC$$

Solution
Question 8
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One end of a thermally insulated rod is kept at a temperature $$T_1$$ and the other at $$T_2$$. The rod is composed of two sections of lengths $$L_1$$ and $$L_2$$ and thermal conductivities $$k_1$$ and $$k_2 $$ respectively. The temperature at the interface of the sections is

A
$$\displaystyle \frac{(K_2L_2T_1+K_1L_1T_2)}{(K_1L_1+K_2L_2)}$$

B
$$\displaystyle \frac{(K_2L_1T_1+K_1L_2T_2)}{(K_2L_1+K_1L_2)}$$

C
$$\displaystyle \frac{(K_1L_2T_1+K_2L_1T_2)}{(K_1L_2+K_2L_1)}$$

D
$$\displaystyle \frac{(K_1L_1T_1+K_2L_2T_2)}{(K_1L_1+K_2L_2)}$$

Solution
Question 9
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Directions For Questions

A nursing home is interested in studying the temperature in $$_{ }^{ o }{ F }$$ when a patient is administered a medicine. The equation $$y={-8x}^{2}+64x-120,x>0$$ gives the relationship between y: the excess of temperature above the normal body temperature $$98.4_{ }^{ o }{ F }$$ measured in $$_{ }^{ o }{ F }$$ and x: the times in hours.

...view full instructions

When is the temperature at its peak? what is its value then?

A
$$4 hrs,106.4^{o}F$$

B
$$3 hrs,102.4^{o}F$$

C
$$2 hrs,104.4^{o}F$$

D
$$1 hrs,98^{o}F$$

Solution
Question 10
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A crystal has a coefficient of expansion $$1.3\times 10^{-8}$$ in one direction and $$2.31\times 10^{-7}$$ in every direction at right angles to it. Then the cubical coefficient of expansion is :

A
$$4.62\times 10^{-7}$$

B
$$2.44\times 10^{-7}$$

C
$$4.75\times 10^{-7}$$

D
$$2.57\times 10^{-7}$$

Solution