Kinetic Theory Test

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Kinetic Theory Test - 90

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Weekly Quiz Competition

Question 1
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The molar heat capacity in a process of a diatomic gas if does a work of $$\frac{Q}{4}$$ when a heat of Q is supplied to is

A
$$\frac{2}{5}R$$

B
$$\frac{5}{2}R$$

C
$$\frac{10}{3}R$$

D
$$\frac{6}{7}R$$

Solution
Question 2
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One mole of an ideal gas passes through a process where pressure and volume obey the relation $$P = P_0 \left[1 - \dfrac{1}{2} \left(\dfrac{V_0}{V} \right)^2 \right]$$. Here $$P_0$$ and $$V_0$$ are constants . Calculate the change in the temperature of the gas if its volume change from $$V_o $$ to $$2 V_o$$.

A
$$\dfrac{1}{2} \dfrac{P_o V_o}{R}$$

B
$$\dfrac{3}{4} \dfrac{P_o V_o}{R}$$

C
$$ \dfrac{5}{4} \dfrac{P_o V_o}{R}$$

D
$$\dfrac{1}{4} \dfrac{P_oV_o}{R}$$

Solution
Question 3
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Three lawn chairs, one made up of aluminium (heat capacity $$=0.90J/K-g$$), one of iron (heat capacity $$=0.45J/K-g$$) and one of tin (heat capacity $$=0.60J/K-g$$) are painted of the same colour. On a sunny day which chair will be hotter to sie?

A
iron chair

B
tin chair

C
aluminium chair

D
all, same

Solution
Question 4
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Directions For Questions

An intimate mixture of hydrogen gas and the theoretical amount of air at $$25^{o}C$$ and a total pressure of $$1\ atm$$, is exposed in a closed rigid vessel. If the process occurs under adiabatic condition, then using the following data, answer the following question :
Given ; $$ (i) C_{P,m} = 8.3\ cal/K-mol\ (ii)\ C_{P, m}= 11.3\ cal/K-mol\ (iii)\ \triangle_{f} H [H_{2}O (g)]= -57.8\ kcal $$$$ (iv)\ Air \ contain \ 20\% O_{2}$$ and $$80\% \ N_{2}$$, by volume

...view full instructions

The values of $$C_{P, m}$$ of $$N_{2}(g)$$ and $$H_{2}O (g)$$ (in $$cal/K-mol$$) should be

A
$$8.3, 8.3$$

B
$$8.3, 11.3$$

C
$$11.3, 11.3$$

D
$$11.3, 8.3$$

Solution
Question 5
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An average human produces about $$10MJ$$ of heat each day through metabolic activity. If a human body were an isolated system of mass $$80kg$$ with the heat capacity of water, what temperature rise would be body experience? Heat capacity of water $$=4.2J/K-g$$

A
$${ 29.76 } K$$

B
$$2.976K$$

C
$${ 2.976\times {{ 10 }^{ 4 } }}^{ o }C$$

D
$${ 0.029 }^{ o }C\quad $$

Solution

heat produced $$=10MJ=10\times {10}^{6}J$$

mass $$=80kg$$

$$C=4.2J/K-g$$

we have relation

$$Q=mc\Delta T$$

$$10\times {10}^{6}=80\times {10}^{3}\times 4.2\times \Delta T$$

$$\Delta T=\cfrac{10\times {10}^{6}}{80\times {10}^{3}\times 4.2}$$

$$\Delta T=0.02976\times {10}^{3}$$

$$\Delta T={29.76} K $$

Option A is correct.
Question 6
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The heat capacity of liquid water is $$75.6J/K-mol$$, while the enthalpy of fusion of ice is $$6.0kJ/mol$$. What is the smallest number of ice cubes at $${0}^{o}C$$, each containing $$9.0g$$ of water, needed to cool $$500g$$ of liquid water from $${20}^{o}C$$ to $${0}^{o}C$$?

A
$$1$$

B
$$7$$

C
$$14$$

D
$$21$$

Solution

$$500g$$ of $${H}_{2}O$$

moles of $${H}_{2}O=\cfrac{500g}{18g/mol}=27.78moles$$

$$Q$$ heat generated $$=mc\Delta T$$

$$=27.78 mol \times 75.6 J/K- mol\times (293-273)K$$

$$=42,000J$$

$$Q=42,000\times \dfrac{1kJ}{1000J}=42kJ/mol$$

Heat of fusion $$=6kJ/mol$$

But we have $$9g$$ $${H}_{2}O$$

moles $$=\cfrac{9g}{18g/mol}=0.5mol$$

So, $$0.5$$ mole of ice (1 ice cube) will have $$3\ kJ$$ of energy.

500g of liquid water contains 42kJ of energy.

9g of water at $$0^oC$$ = 1 ice cube contains 3kJ energy.

So, the number of ice cubes required $$=\dfrac{Total\ energy\ of\ liquid\ water}{energy\ per\ ice\ cube}=\cfrac{42}{3}=14$$

Hence, the correct option is $$C$$
Question 7
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One gram-mole of an ideal gas $$A$$ with the ratio of constant pressure and constant volume specific heats, $$\gamma _A = \dfrac{5}{3}$$ is mixed with $$n$$ gram-moles of another ideal gas $$B$$ with $$\gamma_B = \dfrac{7}{5}$$. If the $$\gamma$$ for the mixture is $$\dfrac{19}{13}$$ what will be the value of $$n$$?

A
$$0.75$$

B
$$2$$

C
$$1$$

D
$$3$$

Solution
Question 8
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In a model of chlorine $$(Cl_2)$$, two $$Cl$$ atoms are rotated about their centre of mass as shown. Here the two $$'CI'$$ atoms are $$2\times 10^{-10}m$$ apart and angular speed $$\omega =2\times 10^{12}\ rad/s$$. If the molar mass of chlorine is $$70\ g/mol$$, then what is the rotational kinetic energy of one $$Cl_2$$ molecule?

A
$$2.32\times 10^{-20}\ J$$

B
$$2.32\times 10^{-21}\ J$$

C
$$2.32\times 10^{-19}\ J$$

D
$$2.32\times 10^{-22}\ J$$

Solution
Question 9
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If at NTP, velocity of sound in a gas is $$1150\ m/s$$, then the $$rms$$ velocity of gas molecules at $$NTP$$ is :( Given : $$R=8.3\ joule/mol/K, C_p=4.8\ cal/mol/K$$)

A
$$1600\ m/s$$

B
$$1532.19\ m/s$$

C
$$160\ m/s$$

D
$$16\ m/s$$

Solution
Question 10
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We would like to increase the length of a $$15\ cm$$ long copper rod of cross-section $$4\ mm^2$$ by $$1\ mm$$. The energy absorbed by the rod if it is heated is $$E_1$$. The energy absorbed by the rod if it is stretched slowly is $$E_2$$. Then $$E_1 /E_2$$ is:

A
$$300$$

B
$$500$$

C
$$480$$

D
$$580$$

Solution