Kinetic Theory Test

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Kinetic Theory Test - 82

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Question 1
1 / -0

Two blocks of the same metal having the same mass and at temperature $$T_1$$ and $$T_2$$, respectively. are brought in contact with each other and allowed to attain thermal equilibrium at constant pressure. The change in entropy, $$\Delta S$$, for this process is :

A
$$2 C_p ln \left(\dfrac{T_1 + T_2}{4T_1 T_2} \right)$$

B
$$2 C_p ln \left[\dfrac{(T_1 + T_2)^{\dfrac{1}{2}}}{T_1 T_2} \right]$$

C
$$C_p ln \left[\dfrac{(T_1 + T_2)^2}{4T_1 T_2} \right]$$

D
$$2C_p ln \left[\dfrac{T_1 + T_2}{2T_1 T_2} \right]$$

Solution

When two blocks are kept in contact with each other, the final temperature will be given as:

$$T_f=\dfrac{T_1+T_2}{2}$$

Now, we have $$\Delta S_{sys}=\int \dfrac{dq_{rev}}{T}=nC_p\int \dfrac{dT}{T}$$

For the first block of metal the entropy will be given as:

$$\Delta S_1=nC_p \int ^{T_f}_{T_1} \dfrac{dT}{T}=nC_pln\dfrac{T_f}{T_1}$$

Similarily, $$\Delta S_2=nC_p ln \dfrac{T_f}{T_2}$$

Now, total change in entropy

$$\Delta S_1+ \Delta S_2 =nC_p \dfrac{{T_f}^2}{T_1 T_2}$$

But , $$T_f=\dfrac{T_1+T_2}{2}$$

$$\therefore$$ Final entropy will be: $$nC_p ln [\dfrac{(T_1+T_2)^2}{4T_1T_2}]$$
Question 2
1 / -0

An ideal gas in a container of volume $$500c.c.$$ is at a pressure of $$2\times 10^5Nm^{-2}$$. The average kinetic energy of each molecule $$6\times 10^{-21}J$$. The number of gas molecules in a container is:

A
$$25\times 10^{25}J$$

B
$$5\times 10^{23}J$$

C
$$25\times 10^{23}J$$

D
$$2.5\times 10^{22}J$$

Solution
Question 3
1 / -0

One mole of monoatomic gas is carried along process ABCDEA as shown in the diagram.Find the net work done by gas.

A
$$ \frac {3}{2} J $$

B
1 J

C
$$ \frac {1}{2} J $$

D
0 J

Solution
Question 4
1 / -0

At 323 K, the vapour pressure in millimeters of mercury of a methanol-ethanol solution is represented by the equation $$p=120{ x }_{ A }+140$$,where $${ x }_{ A }$$ is the mole fraction of methanol. Then the value of $$\lim _{ { X }_{ A }\rightarrow 1 }{ \frac { { P }_{ A } }{ { X }_{ A } } } $$

A
250 mm

B
140 mm

C
260 mm

D
20 mm

Solution
Question 5
1 / -0

From the following data of $$\Delta H$$, of the following reactions,

$$C(s) + \dfrac{1}{2}O_2 (g) \rightarrow CO (g)$$ $$\Delta H = -110 kJ$$

$$C(s) + H_2O (g) \rightarrow CO (g) + H_2 (g)$$ $$\Delta H = 132 kJ$$

What is the mole composition of the mixture of steam and oxygen on being passed over a coke at 1273 K, keeping temperature constant?

A
0.5 : 1

B
0.6 : 1

C
0.8 : 1

D
1 : 1

Solution
Question 6
1 / -0

Three lawn chairs, one made up of aluminium (heat capacity $$= 0.90\ J/K-g$$), one of iron (heat capacity $$= 0.45\ J/K-g$$) and one of tin (heat capacity$$ = 0.60\ J/K-g$$) are painted of the same colour. On a sunny day which chair will be hotter to sit?

A
Iron chair

B
tin chair

C
aluminium chair

D
all, same

Solution
Question 7
1 / -0

One kg of a diatomic gas is at a pressure of $$ 8\times 10^{4}\mathrm{N}/\mathrm{m}^{2}$$. The density of the gas is 4 $$\mathrm{k}\mathrm{g}/\mathrm{m}^{3}$$. The energy of the gas due to its thermal motion will be

A
$$3 \times 10^4 $$ J

B
$$5 \times 10^4$$ J

C
$$6 \times 10^4$$ J

D
$$7 \times 10^4$$ J

Solution
Question 8
1 / -0

Three closed vessels A, B and C are at the same temperature T and contain gases which obey the Maxwellian distribution of velocities, Vessel A contains only $${ O }_{ 2 }$$ B only $${ N }_{ 2 }$$ and C a mixture of equal quantities of $${ O }_{ 2 }$$ and $${ N }_{ 2 }$$ If the average speed of the $${ O }_{ 2 }$$ molecules in vessel A is $${ V }_{ 1 }$$, that of $$N_{ 2 }$$ molecules in vessel B is $$V_{ 2 }$$ the average speed of the $$O_{ 2 }$$ molecules in vessel C is ( where M is the mass of an oxygen molecule)

A
$$\left( { V }_{ 1 }+{ V }_{ 2 } \right) /2$$

B
$${ V }_{ 1 }$$

C
$$\left( { V }_{ 1 }{ V }_{ 2 } \right) ^{ 1/2 }$$

D
$$\sqrt { 3kT/M } $$

Solution
Question 9
1 / -0

The value of universal gas constant is $$R=8.3$$ J/K - mol. The value of $$R$$ in atmosphere litre per kelvin mol

A
$$8.12$$

B
$$0.00812$$

C
$$81.2$$

D
$$0.082$$

Solution
Question 10
1 / -0

For monoatomic gas the relation between pressure of a gas and temperature T is given by $$P_\alpha T^C$$. Then value of C will be : (For adiabatic process)

A
$$\dfrac{5}{3}$$

B
$$\dfrac{2}{5}$$

C
$$\dfrac{3}{5}$$

D
$$\dfrac{5}{2}$$

Solution