Thermal Properties of Matter Test

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Thermal Properties of Matter Test - 49

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Question 1
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A glass flask is filled up to a mark with $$50\ cc$$of mercury at $${18}^{o}C$$. If the flask and content are heated to $${38}^{o}C$$, how much mercury will be above the mark? ($$\alpha$$ for glass is $$9\times { { 10 }^{ -6 } }/{ C }$$ and coefficient of real expansion of mercury is $$180\times { { 10 }^{ -6 } }/{ C })$$

A
$$0.85\ cc$$

B
$$0.46\ cc$$

C
$$0.153\ cc$$

D
$$0.05\ cc$$

Solution

Volume expansion coefficient of glass$$=3\times linear =3\alpha$$
Change in temperature is $$38-18=20^0 C$$
Increment of volume of flask is $$\Delta V=50cc\times 3\alpha \times 20^0 C=0.027cc$$

Expansion in mercury $$50cc \times \gamma \Delta t=50\times 180\times 10^{-6}\times 20=0.180cc$$

Apparent increment=$$0.180-0.027=0.153cc$$
Option C is correct.
Question 2
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$$0.1\,{m^3}$$ of water at $$80^\circ C$$ is mixed with $$0.3\,{m^3}$$ of water at $$60^\circ C$$. The final temperature of the mixture is :

A
$$65^\circ C$$

B
$$70^\circ C$$

C
$$60^\circ C$$

D
$$75^\circ C$$

Solution

Given volume of water $${V}_{1}=0.1 {m}^{3}$$ and initial temperature$${T}_{1}={80}^{0}C$$ and volume $${V}_{2}=0.3 {m}^{3}$$ and $${T}_{2}={60}^{0}C$$
Thus
$${m}_{1}{c}_{p}{dt}_{1}={m}_{2}{c}_{p}{dt}_{2}$$
as we know $$m=\rho V$$
$$\rho (0.1){c}_{p}(80-{T}_{f})=\rho (0.3){c}_{p}({T}_{f}-60)$$
$$4{T}_{f}=260$$
$${T}_{f}={65}^{0}C$$
Question 3
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When $$500 kg$$ of water is heated from $$20^oC$$ to $$100^oC$$, then the increase in mass of water will be

A
$$3.2\times { 10 }^{ -9 }$$

B
$$1.87\times { 10 }^{ -9 }$$

C
$$0.96\times { 10 }^{ -9 }$$

D
$$2.8\times { 10 }^{ -9 }$$

Solution
Question 4
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Ratio of radius of curvature of cylindrical emitters of same type is $$1:4$$ and their temp. are in ration $$2:1$$. Then ration of amount of heat emitted by them is-(For Cylinder length = radius);-

A
2:1

B
1:1

C
4:1

D
1:4

Solution
Question 5
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Q.1 the frame is made by seven meter wire, each has conductivity K. length of each segment is $$ \ell $$ l 2. The temperature of points E,F and A are maintained at $$ 160^o $$ c,$$ 200^oC $$ and $$ 100^oC $$ respectively.(assume heat flows through the wire only and there is no loss of heat from the side of the wire).Then the tempera-ture at C is ( approx).

A
$$ 135^oC $$

B
$$ 124^oC $$

C
$$ 120^oC $$

D
$$ 112^oC $$

Solution
Question 6
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Temperature of a room is maintained at $$20^{\circ}$$ by a heater of power $$2\ kW$$. The room has a glass window of area $$1\ m^{2}$$, thickness $$0.2\ cm$$ and thermal conductivity $$0.2\ cal/m/^{\circ}C/s$$. Temperature of outside is about.

A
$$-63.6^{\circ}C$$

B
$$15^{\circ}C$$

C
$$20^{\circ}C$$

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

Solution

If temperature of outside be $$\theta $$ then putting $$k=0.2, A=1m^2 , l=.002meter$$
and $$H=2kW=2000J/s=2000\times 4.18 cal/s =8360cal/s$$
in the formula $$H=KA\dfrac{20-\theta }{l}$$, we get $$20-\theta =83.6^0 C$$
so $$\theta =-63.6^0 C$$
Question 7
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An ideal gas has an initial volume $$V$$ and pressure $$P$$. In doubling its volume the minimum work done will be in (of the given processes):

A
Isobaric process

B
Isothermal process

C
Adiabatic process

D
Same in all given processes

Solution

The isothermal case delivers more work because it has heat supplied to it, some fraction of which is converted to work. But for a given increment in volume, the adiabatic case begins to deliver more work. In the adiabatic case, as the volume fraction approaches infinity, the specific volume is made smaller by the fact that the temperature must decrease, but this is not the case for the isothermal expansion.
Answer B:
Question 8
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In case of heat flow across the composite rod shown above, temperature $$\theta$$ is

A
$$80^{\circ}C$$

B
$$-80^{\circ}C$$

C
$$0^{\circ}C$$

D
$$-20^{\circ}C$$

Solution

Rods have been joined in series so the heat rate should be same in both the rods.
The heat rate in the thick rod is $$H_1=(3K)(2A)\dfrac{(80-40)}{2L}=120KA/L$$
For the thin rod the heat rate will be $$H_2=KA\dfrac{40-\theta}{L}$$
Both $$H_1$$ and $$H_2$$ should be equal so $$40-\theta=120$$ so $$\theta =-80^0C$$
Option B is correct.
Question 9
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A vessel contains 28 gm of $$N-2$$ and 32 gm of $$O_2$$ at temperature T = 1800 K and pressure 2 atm pressure it $$N_2$$ dissociates $$30%$$ and $$O_2$$ dissociates $$50%$$ if temperature remains constant.

A
2 atm

B
1 atm

C
2.8 atm

D
1.4 atm
Question 10
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Which of the following statements is true for a thermometer?

A
Coefficient of cubical expansion of liquid must be greater than that of bulb material

B
Coefficient of cubical expansion of liquid may be equal to that of bulb material

C
Coefficient of cubical expansion of liquid must be less than of bulb material

D
None of the above

Solution

During the heat transfer from a body to the thermometer, the bulb and the liquid in the thermometer both expand. The expansion of the liquid must be greater than that of the bulb because the liquid has to rise in the capillary tube.
Therefore, the coefficient of cubical expansion of the liquid must be greater than that of the bulb material.
The correct option is A.