Kinetic Theory Test

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Kinetic Theory Test - 32

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Weekly Quiz Competition

Question 1
1 / -0

Assertion: PV/T=constant for 1 gram of gas. This constant varies from gas to gas.
Reason:1 gram of different gases at NTP occupy different volumes.

A
Both assertion (A) and reason (R) are correct and R gives the correct explanation

B
Both assertion (A) and reason (R) are correct but R doesnt give the correct explanation

C
A is true but R is false

D
A is false but R is true

Solution

As different type of gases will have different molecular mass therefore, gases will occupy different volumes also
Hence assertion is true and reason is correct explaination
option (A)
Question 2
1 / -0

To find out degree of freedom, the correct expression is :

A
$$f=\dfrac { 2 }{ \gamma -1 }$$

B
$$f=\dfrac { \gamma +1 }{ 2 }$$

C
$$f=\dfrac { 2 }{ \gamma +1 }$$

D
$$f=\dfrac { 1 }{ \gamma +1 }$$

Solution

$$\because \gamma =1+\dfrac { 2 }{ f } $$
$$\Longrightarrow \dfrac { 2 }{ f } =\gamma -1\Longrightarrow f=\dfrac { 2 }{ \gamma -1 } $$
Question 3
1 / -0

A vessel contains air and saturated vapor. The pressure of air is $$\mathrm{p}_{2}$$ and $$\mathrm{p}_{1}$$ is the S.V. P. On compressing the mixture to one-fourth of its original volume, what is the increase in pressure of the mixture?

A
$$2\mathrm{p}_{1}$$

B
$$2\mathrm{p}_{2}$$

C
$$3\mathrm{p}_{1}$$

D
$$3\mathrm{p}_{2}$$

Solution

Initially total pressure $$=(P_{1}+P_{2})$$
When compressed to $$\dfrac{1}{4}$$ of its volume, the pressure of air becomes $$4P_{2}.$$
Pressure of saturated vapour remains the same.
Total pressure after compression $$=4P_{2}+P_{1}$$
Difference in pressure$$=(4P_{2}+P_{1})-(P_{1}+P_{2})$$
$$=3P_{2}$$
Question 4
1 / -0

Match List I with List II
List-I                                               List-II
a) 0.00366/$$^{0}$$ C                   e) Avagadros Number
b) 6.023x10$$^{23}$$ molecules   f) Universal gas constant
c) -273$$^{0}$$ C g) Pressure coefficient of gas
d) 8.31 J/K-mole h) Intercept of V-T graph at
                                                  constnat pressure

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

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

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

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

Solution

(a)$$0.00366^{o}C$$ = $$\frac{1}{273}^{o}C$$ = pressure coefficient of gas
a - g
(b)$$6.023 \times {10}^{23}$$ is Avagadros Number.
b - e
(c)$$-273^{o}C$$ is Intercept of V-T graph at constnat pressure(as shown in image)
c - h
(d)8.31 J/K-mole is Universal gas constant(R).
d - f
Answer is A.
Question 5
1 / -0

Match List I and List II
List-I List-II
a) P-V graph(T is constant) e) St. line cutting temp axis at - 273$$^{0}$$
b) P-T graph(V is constant) f) Rectangular hyperbola
c) V-T graph(pressure P is constant) g) A st.line parallel to axis
d) PV- P garph h) St. line passing trhough origin (T is constant)

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

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

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

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

Solution

(a) P-V graph (T is constant):
$$PV = nRT$$
at constant temperature
$$PV = constant$$
$$P \alpha \frac{1}{V}$$
so it will be Rectangular hyperbola.

(b) P-T Graph (V is constant) :
$$PV = nRT$$
at constant volume
$$P \alpha T$$
pressure is proportional to T, so it will be straight line passing through origin.

c) V-T graph(P is constant) :
$$PV = nRT$$
at constant pressure
$$V \alpha T$$
volume is proportional to T(Kelvin),so it will be straight line passing through origin, but if temperature is taken in $$^{o}C$$, then it will cut temperature axis at $$-273 ^{o}C$$

(d) PV - P Graph (T is constant) :
$$PV = nRT$$
at constant Temperature
$$PV = constant$$
$$PV$$ is constant for constant temperature,so it will be straight line parallel to P axis.
Question 6
1 / -0

The amount of heat energy required to raise the temperature of $$1\ g$$ of Helium at NTP, from $$T_1K$$ to $$T_2K$$ is -

A
$$\displaystyle \dfrac{3}{2}N_a k_B (T_2 - T_1)$$

B
$$\displaystyle \dfrac{3}{4}N_a k_B (T_2 - T_1)$$

C
$$\displaystyle \frac{3}{4}N_a k_B (\frac{T_2}{T_1})$$

D
$$\displaystyle \frac{3}{8}N_a k_B (T_2 - T_1)$$

Solution
Question 7
1 / -0

At change of state the kinetic energy of the molecules of a substances increases greatly.

A
True

B
False

C
Either

D
Neither

Solution

False.
If heat is coming into a substance during a phase change, then this energy is used to break the bonds between the molecules of the substance.
An example we will use here is ice melting into water.
Question 8
1 / -0

At pressure P and absolute temperature T a mass M of an ideal gas fills a closed container of volume V. An additional mass 2M of the same gas is added into the container and the volume is then reduced to $$\dfrac{v}{3}$$ and the temperature to $$\dfrac{T}{3}.$$ The pressure of the gas will now be :

A
$$\dfrac{P}{3}$$

B
$$P$$

C
$$3 P$$

D
$$9 P$$

Solution

If $$M_{0}$$ is molecular mass of the gas then for initial condition PV
$$=\dfrac{M}{M_{0}}.RT ........(1)$$
After 2M mass has been added
$${P}'.\dfrac{V}{3}=\dfrac{3M}{M_{0}}.R.\frac{T}{3} .........(2)$$
By dividing (2) and (1)
$${P}'=3P$$
Question 9
1 / -0

Producers gas is a mixture of

A
Carbon monoxide and nitrogen gas

B
Carbon monoxide and hydrogen gas

C
Carbon monoxide and water vapour

D
Carbon monoxide and nitrous oxide

Solution
Question 10
1 / -0

Atom of an element is electrically

A
Positive

B
Negative

C
Neutral

D
None of these

Solution

According to Thomson's model of an atom,
Atom as a whole is electrically neutral because the negatively charged electrons and positively charged protons are equal in magnitude and, thus, atom as a whole is electrically neutral.
Hence, the correct option is C.

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Kinetic Theory Test - 32

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Kinetic Theory Test - 32

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Question 1

Both assertion (A) and reason (R) are correct and R gives the correct explanation

Both assertion (A) and reason (R) are correct but R doesnt give the correct explanation

A is true but R is false

A is false but R is true

Solution

Question 2

$$f=\dfrac { 2 }{ \gamma -1 }$$

$$f=\dfrac { \gamma +1 }{ 2 }$$

$$f=\dfrac { 2 }{ \gamma +1 }$$

$$f=\dfrac { 1 }{ \gamma +1 }$$

Solution

Question 3

$$2\mathrm{p}_{1}$$

$$2\mathrm{p}_{2}$$

$$3\mathrm{p}_{1}$$

$$3\mathrm{p}_{2}$$

Solution

Question 4

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

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

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

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

Solution

Question 5

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

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

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

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

Solution

Question 6

$$\displaystyle \dfrac{3}{2}N_a k_B (T_2 - T_1)$$

$$\displaystyle \dfrac{3}{4}N_a k_B (T_2 - T_1)$$

$$\displaystyle \frac{3}{4}N_a k_B (\frac{T_2}{T_1})$$

$$\displaystyle \frac{3}{8}N_a k_B (T_2 - T_1)$$

Solution

Question 7

True

False

Either

Neither

Solution

Question 8

$$\dfrac{P}{3}$$

$$P$$

$$3 P$$

$$9 P$$

Solution

Question 9

Carbon monoxide and nitrogen gas

Carbon monoxide and hydrogen gas

Carbon monoxide and water vapour

Carbon monoxide and nitrous oxide

Solution

Question 10

Positive

Negative

Neutral

None of these

Solution

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