Thermal Properties of Matter Test

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Thermal Properties of Matter Test - 10

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Question 1
1 / -0

$$0.5$$ moles of an ideal gas at constant temperature $$27^{\circ}C$$ kept inside a cylinder of length $$L$$ and cross-section area $$A$$ closed by a massless piston.
The cylinder is attached with a conducting rod of length $$L$$, cross-section area $$(\dfrac{1}{9})m^{2}$$ and thermal conductivity $$k$$, whose other end is maintained at $$0^{\circ}C$$. If piston is moved such that rate of heat flow through the conducing rod is constant then velocity of piston when it is at height $$\dfrac{L}{2}$$ from the bottom of cylinder is:
[Neglect any kind of heat loss from system]

A
$$\left (\dfrac {k}{R}\right )m/sec$$

B
$$\left (\dfrac {k}{10R}\right )m/sec$$

C
$$\left (\dfrac {k}{100R}\right )m/sec$$

D
$$\left (\dfrac {k}{1000R}\right )m/sec$$

Solution

$$\dfrac {\triangle Q}{\triangle t} = \dfrac {\triangle W}{\triangle t} =$$ work done per unit time $$= \dfrac {ka\theta}{L}$$
$$\dfrac {dW}{dt} = P \dfrac {dv}{dt} = k \dfrac {a\theta}{L}, P = \dfrac {nRT}{V}$$
$$\Rightarrow \dfrac {0.5R(300}{V} A. \dfrac {dl}{dt} = \dfrac {ka\theta}{L}$$
$$\Rightarrow \dfrac {0.5R(300)}{A.\dfrac {L}{2}}A.v = \dfrac {ka\theta}{L}$$
$$\Rightarrow v = \dfrac {ka}{R}\left (\dfrac {27}{300}\right ) = \dfrac {k}{100R}$$.
Question 2
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The difference between volume and pressure coefficients of an ideal gas is :

A
$$\dfrac{1}{273}$$

B
$$273$$

C
$$\dfrac{2}{273}$$

D
Zero

Solution

Volume coefficient: $$\alpha$$
Pressure coefficient: $$\beta$$
$$\alpha=\beta=\frac{1}{273}$$
Question 3
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A sealed glass jar is full of water. When it is kept in a freezing mixture, it is broken because :

A
water expands from $$4^{o}C$$ to $$0^{o}C$$

B
ice expands while melting

C
water expands due to freezing

D
ice expands since its temperature falls below $$0^{0}C$$

Solution

Anomalous expansion of water occurs when cooled from $$4^0$$C to $$0^0$$C.
Hence, the sealed glass jar will be broken.
Question 4
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The gas law $$\left [ \dfrac{PV}{T} \right ]=$$ constant is true for

A
isothermal change only

B
adiabatic change only

C
both isothermal & adiabatic

D
neither isothermal nor adiabatic

Solution

The given relation is always valid for ideal gas whether the process is adiabatic or isothermal because its the fundamental equation of ideal gas.
$$P \times V=n \times R \times T$$
Question 5
1 / -0

List - I                                         List - II
a. Temperature of water          e.273 K
at the bottom of a lake
b.$$\gamma _{r}$$of water is - ve                    f. 277 K
between
c. $$\gamma _{r}$$ of water is positive        g. above 277 K
d. Temperature of water           h. 273K and
just below ice layer in                277 K
a Lake

A
a- g, b-h, c-e, d-f

B
a-h, b-e, c-f, d-g

C
a-e, b-f, c-g, d-h

D
a-f, b-h, c-g, d-e

Solution

Water has maximum density at $$4^{\circ}C=277K$$. Hence water at this temperature is settled at the bottom.
Below this temperature, liquid water has negative coefficient of expansion. Hence as ice is melted, the volume of water initially decreases.
Question 6
1 / -0

Water at $$4^{0}$$C is filled to the brim of 2 beakers. A boy performed an experiment A of heating and B of cooling. The observation was :

A
water level in B went down and in A water flowed out

B
water flowed out in both the cases

C
water flowed out in B and water level went down in A

D
water level went down in both cases

Solution

Water has anomalous expansion from $$4^0$$C to $$0^0$$C.
Water expands when heated from $$4^0$$C onwards.
Since water expands in both the cases, it will overflow from both experiments A and B.
Question 7
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The P-T graph for the given mass of an ideal gas is shown in figure. Then the volume

A
increases

B
decreases

C
remains constant

D
data insufficient

Solution

From the graph it is clear that P is directly proportional to T. For an ideal gas it happens, when volume remains constant.
Question 8
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A gas in an airtight container is heated from 25$$^{o}$$C to 90$$^{o}$$C. The density of gas will :

A
increase slightly

B
increase considerably

C
remain the same

D
decrease slightly

Solution

Since the container is airtight, volume will remain same, hence the density will remain same.
Question 9
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A sealed glass jar is full of water. When its temperature is decreased to $$0^{o}C$$ :

A
The glass jar remains as it is with ice

B
The glass jar remains as it is with water

C
The glass jar contains half the amount of ice mixed with water

D
The glass jar breaks due to the formation of ice

Solution

From $$4^0$$C to $$0^0$$C water will expand. while ice is getting formed.
Hence, the glass jar will break.
Question 10
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The molar gas constant is the same for all gases because at the same temperature and pressure, equal volumes of gases have the same :

A
number of molecules

B
average potential energy

C
ratio of specific heats

D
density

Solution

We know, $$R=\frac { PV }{ nT } $$
assuming P,V and T to be constant.
Also we know, that equal volume of gases contain equal number of molecules, hence the value of R is also constant.