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PHXI13:KINETIC THEORY

360350 $4.0 g$ of gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is $5.0 J K^{- 1} m o l^{- 1}$ . If the speed of sound in this gas at NTP is $999 m s^{- 1}$ then the specific heat capacity at constant pressure in $J k^{- 1} m o l^{- 1}$ is (Take gas $R = 8.3 J K^{- 1} m o l^{- 1})$

1 8

2 7

3 6.5

4 6

Explanation:

As the given conditions are at NTP $m = M = 4.0 g$
(As it occupies 22.4 liters)
$v_{r m s} = 999 m / s R = 8.3 J \cdot k^{- 1} m o l^{- 1}$
$v_{r m s} = \sqrt{\frac{γ R T}{M}} \Rightarrow γ = \frac{M v^{2}}{R T} = 1.6$
$γ = \frac{C_{P}}{C_{V}} \Rightarrow C_{P} = γ C_{V} = 1.6 \times 5 = 8 J . k^{- 1} m o l^{- 1}$

PHXI13:KINETIC THEORY

360351 If $γ$ is the ratio of specific heats and $R$ is the universal gas constant, then the molar specific heat at constant volume $C_{v}$ is given by

1

\frac{R}{γ - 1}

2

\frac{γ R}{γ - 1}

3

γ R

4

\frac{(γ - 1) R}{γ}

Explanation:

We know that
$\frac{C_{p}}{C_{v}} = γ (1)$
But
$C_{p} - C_{v} = R (2)$
(2)
From (1) & (2)
$γ C_{v} - C_{v} = R \Rightarrow C_{v} = \frac{R}{γ - 1}$

PHXI13:KINETIC THEORY

360352 $C_{P}$ and $C_{V}$ are specific heats at constant pressure and constant volume respectively. It is observed that $C_{p} - C_{v} = a$ for hydrogen gas $C_{p} - C_{v} = b$ for nitrogen gas. The correct relation between $a$ and $b$ :

1

a = 14 b

2

a = 28 b

3

a = \frac{1}{14} b

4

a = b

Explanation:

Molar specific heat $C^{'} = \frac{Δ Q}{n Δ T}$
Specific heat $C = \frac{Δ Q}{m Δ T}$
$\begin{aligned} \frac{C^{'}}{C} = \frac{m}{n} = M (Molecular weight) \\ C = \frac{C^{'}}{M} \\ C_{P}^{'} - C_{V}^{'} = R \\ M C_{P} - M C_{V} = R \\ C_{P} - C_{V} = \frac{R}{M} \end{aligned}$
For hydrogen $M = 2$
$C_{P} - C_{V} = \frac{R}{2} = a$
For nitrogen $M = 28$
$\begin{aligned} \Rightarrow C_{P} - C_{V} = \frac{R}{28} = b \\ \frac{a}{b} = 14 \end{aligned}$

PHXI13:KINETIC THEORY

360353 For an ideal gas of diatomic molecules

1

C_{P} = \frac{5}{2} R

2

C_{V} = \frac{3}{2} R

3

C_{P} - C_{V} = 2 R

4

C_{P} = \frac{7}{2} R

Explanation:

$C_{P} = (\frac{f}{2} + 1) R = (\frac{5}{2} + 1) R = \frac{7}{2} R$

PHXI13:KINETIC THEORY

360354 Statement A :
The ratio of specific heat of a gas at constant pressure and specific heat at constant volume for a diatomic gas is more than that for a monoatomic gas
Statement B :
The molecules of a monoatomic gas have more degree of freedom than those of a diatomic gas.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both statements are correct.

4 Both Statements are incorrect.

Explanation:

For a monoatomic gas, number of degree of freedom $f = 3$ , and for a diatomic gas, $f = 5$ ,
As, $\frac{C_{P}}{C_{V}} = γ = 1 + \frac{2}{f}$
For monoatomic gas, $\frac{C_{P}}{C_{V}} = \frac{5}{3} = 1.67$ and
For diatomic gas, $\frac{C_{P}}{C_{V}} = \frac{7}{5} = 1.4$
${(\frac{C_{P}}{C_{V}})}_{monoatomic} > {(\frac{C_{P}}{C_{V}})}_{diatomic}$
Both statements are wrong. So option (4) is correct.

PHXI13:KINETIC THEORY

360350 $4.0 g$ of gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is $5.0 J K^{- 1} m o l^{- 1}$ . If the speed of sound in this gas at NTP is $999 m s^{- 1}$ then the specific heat capacity at constant pressure in $J k^{- 1} m o l^{- 1}$ is (Take gas $R = 8.3 J K^{- 1} m o l^{- 1})$

1 8

2 7

3 6.5

4 6

Explanation:

As the given conditions are at NTP $m = M = 4.0 g$
(As it occupies 22.4 liters)
$v_{r m s} = 999 m / s R = 8.3 J \cdot k^{- 1} m o l^{- 1}$
$v_{r m s} = \sqrt{\frac{γ R T}{M}} \Rightarrow γ = \frac{M v^{2}}{R T} = 1.6$
$γ = \frac{C_{P}}{C_{V}} \Rightarrow C_{P} = γ C_{V} = 1.6 \times 5 = 8 J . k^{- 1} m o l^{- 1}$

PHXI13:KINETIC THEORY

360351 If $γ$ is the ratio of specific heats and $R$ is the universal gas constant, then the molar specific heat at constant volume $C_{v}$ is given by

1

\frac{R}{γ - 1}

2

\frac{γ R}{γ - 1}

3

γ R

4

\frac{(γ - 1) R}{γ}

Explanation:

We know that
$\frac{C_{p}}{C_{v}} = γ (1)$
But
$C_{p} - C_{v} = R (2)$
(2)
From (1) & (2)
$γ C_{v} - C_{v} = R \Rightarrow C_{v} = \frac{R}{γ - 1}$

PHXI13:KINETIC THEORY

360352 $C_{P}$ and $C_{V}$ are specific heats at constant pressure and constant volume respectively. It is observed that $C_{p} - C_{v} = a$ for hydrogen gas $C_{p} - C_{v} = b$ for nitrogen gas. The correct relation between $a$ and $b$ :

1

a = 14 b

2

a = 28 b

3

a = \frac{1}{14} b

4

a = b

Explanation:

Molar specific heat $C^{'} = \frac{Δ Q}{n Δ T}$
Specific heat $C = \frac{Δ Q}{m Δ T}$
$\begin{aligned} \frac{C^{'}}{C} = \frac{m}{n} = M (Molecular weight) \\ C = \frac{C^{'}}{M} \\ C_{P}^{'} - C_{V}^{'} = R \\ M C_{P} - M C_{V} = R \\ C_{P} - C_{V} = \frac{R}{M} \end{aligned}$
For hydrogen $M = 2$
$C_{P} - C_{V} = \frac{R}{2} = a$
For nitrogen $M = 28$
$\begin{aligned} \Rightarrow C_{P} - C_{V} = \frac{R}{28} = b \\ \frac{a}{b} = 14 \end{aligned}$

PHXI13:KINETIC THEORY

360353 For an ideal gas of diatomic molecules

1

C_{P} = \frac{5}{2} R

2

C_{V} = \frac{3}{2} R

3

C_{P} - C_{V} = 2 R

4

C_{P} = \frac{7}{2} R

Explanation:

$C_{P} = (\frac{f}{2} + 1) R = (\frac{5}{2} + 1) R = \frac{7}{2} R$

PHXI13:KINETIC THEORY

360354 Statement A :
The ratio of specific heat of a gas at constant pressure and specific heat at constant volume for a diatomic gas is more than that for a monoatomic gas
Statement B :
The molecules of a monoatomic gas have more degree of freedom than those of a diatomic gas.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both statements are correct.

4 Both Statements are incorrect.

Explanation:

For a monoatomic gas, number of degree of freedom $f = 3$ , and for a diatomic gas, $f = 5$ ,
As, $\frac{C_{P}}{C_{V}} = γ = 1 + \frac{2}{f}$
For monoatomic gas, $\frac{C_{P}}{C_{V}} = \frac{5}{3} = 1.67$ and
For diatomic gas, $\frac{C_{P}}{C_{V}} = \frac{7}{5} = 1.4$
${(\frac{C_{P}}{C_{V}})}_{monoatomic} > {(\frac{C_{P}}{C_{V}})}_{diatomic}$
Both statements are wrong. So option (4) is correct.

PHXI13:KINETIC THEORY

360350 $4.0 g$ of gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is $5.0 J K^{- 1} m o l^{- 1}$ . If the speed of sound in this gas at NTP is $999 m s^{- 1}$ then the specific heat capacity at constant pressure in $J k^{- 1} m o l^{- 1}$ is (Take gas $R = 8.3 J K^{- 1} m o l^{- 1})$

1 8

2 7

3 6.5

4 6

Explanation:

As the given conditions are at NTP $m = M = 4.0 g$
(As it occupies 22.4 liters)
$v_{r m s} = 999 m / s R = 8.3 J \cdot k^{- 1} m o l^{- 1}$
$v_{r m s} = \sqrt{\frac{γ R T}{M}} \Rightarrow γ = \frac{M v^{2}}{R T} = 1.6$
$γ = \frac{C_{P}}{C_{V}} \Rightarrow C_{P} = γ C_{V} = 1.6 \times 5 = 8 J . k^{- 1} m o l^{- 1}$

PHXI13:KINETIC THEORY

360351 If $γ$ is the ratio of specific heats and $R$ is the universal gas constant, then the molar specific heat at constant volume $C_{v}$ is given by

1

\frac{R}{γ - 1}

2

\frac{γ R}{γ - 1}

3

γ R

4

\frac{(γ - 1) R}{γ}

Explanation:

We know that
$\frac{C_{p}}{C_{v}} = γ (1)$
But
$C_{p} - C_{v} = R (2)$
(2)
From (1) & (2)
$γ C_{v} - C_{v} = R \Rightarrow C_{v} = \frac{R}{γ - 1}$

PHXI13:KINETIC THEORY

360352 $C_{P}$ and $C_{V}$ are specific heats at constant pressure and constant volume respectively. It is observed that $C_{p} - C_{v} = a$ for hydrogen gas $C_{p} - C_{v} = b$ for nitrogen gas. The correct relation between $a$ and $b$ :

1

a = 14 b

2

a = 28 b

3

a = \frac{1}{14} b

4

a = b

Explanation:

Molar specific heat $C^{'} = \frac{Δ Q}{n Δ T}$
Specific heat $C = \frac{Δ Q}{m Δ T}$
$\begin{aligned} \frac{C^{'}}{C} = \frac{m}{n} = M (Molecular weight) \\ C = \frac{C^{'}}{M} \\ C_{P}^{'} - C_{V}^{'} = R \\ M C_{P} - M C_{V} = R \\ C_{P} - C_{V} = \frac{R}{M} \end{aligned}$
For hydrogen $M = 2$
$C_{P} - C_{V} = \frac{R}{2} = a$
For nitrogen $M = 28$
$\begin{aligned} \Rightarrow C_{P} - C_{V} = \frac{R}{28} = b \\ \frac{a}{b} = 14 \end{aligned}$

PHXI13:KINETIC THEORY

360353 For an ideal gas of diatomic molecules

1

C_{P} = \frac{5}{2} R

2

C_{V} = \frac{3}{2} R

3

C_{P} - C_{V} = 2 R

4

C_{P} = \frac{7}{2} R

Explanation:

$C_{P} = (\frac{f}{2} + 1) R = (\frac{5}{2} + 1) R = \frac{7}{2} R$

PHXI13:KINETIC THEORY

360354 Statement A :
The ratio of specific heat of a gas at constant pressure and specific heat at constant volume for a diatomic gas is more than that for a monoatomic gas
Statement B :
The molecules of a monoatomic gas have more degree of freedom than those of a diatomic gas.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both statements are correct.

4 Both Statements are incorrect.

Explanation:

For a monoatomic gas, number of degree of freedom $f = 3$ , and for a diatomic gas, $f = 5$ ,
As, $\frac{C_{P}}{C_{V}} = γ = 1 + \frac{2}{f}$
For monoatomic gas, $\frac{C_{P}}{C_{V}} = \frac{5}{3} = 1.67$ and
For diatomic gas, $\frac{C_{P}}{C_{V}} = \frac{7}{5} = 1.4$
${(\frac{C_{P}}{C_{V}})}_{monoatomic} > {(\frac{C_{P}}{C_{V}})}_{diatomic}$
Both statements are wrong. So option (4) is correct.

PHXI13:KINETIC THEORY

360350 $4.0 g$ of gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is $5.0 J K^{- 1} m o l^{- 1}$ . If the speed of sound in this gas at NTP is $999 m s^{- 1}$ then the specific heat capacity at constant pressure in $J k^{- 1} m o l^{- 1}$ is (Take gas $R = 8.3 J K^{- 1} m o l^{- 1})$

1 8

2 7

3 6.5

4 6

Explanation:

As the given conditions are at NTP $m = M = 4.0 g$
(As it occupies 22.4 liters)
$v_{r m s} = 999 m / s R = 8.3 J \cdot k^{- 1} m o l^{- 1}$
$v_{r m s} = \sqrt{\frac{γ R T}{M}} \Rightarrow γ = \frac{M v^{2}}{R T} = 1.6$
$γ = \frac{C_{P}}{C_{V}} \Rightarrow C_{P} = γ C_{V} = 1.6 \times 5 = 8 J . k^{- 1} m o l^{- 1}$

PHXI13:KINETIC THEORY

360351 If $γ$ is the ratio of specific heats and $R$ is the universal gas constant, then the molar specific heat at constant volume $C_{v}$ is given by

1

\frac{R}{γ - 1}

2

\frac{γ R}{γ - 1}

3

γ R

4

\frac{(γ - 1) R}{γ}

Explanation:

We know that
$\frac{C_{p}}{C_{v}} = γ (1)$
But
$C_{p} - C_{v} = R (2)$
(2)
From (1) & (2)
$γ C_{v} - C_{v} = R \Rightarrow C_{v} = \frac{R}{γ - 1}$

PHXI13:KINETIC THEORY

360352 $C_{P}$ and $C_{V}$ are specific heats at constant pressure and constant volume respectively. It is observed that $C_{p} - C_{v} = a$ for hydrogen gas $C_{p} - C_{v} = b$ for nitrogen gas. The correct relation between $a$ and $b$ :

1

a = 14 b

2

a = 28 b

3

a = \frac{1}{14} b

4

a = b

Explanation:

Molar specific heat $C^{'} = \frac{Δ Q}{n Δ T}$
Specific heat $C = \frac{Δ Q}{m Δ T}$
$\begin{aligned} \frac{C^{'}}{C} = \frac{m}{n} = M (Molecular weight) \\ C = \frac{C^{'}}{M} \\ C_{P}^{'} - C_{V}^{'} = R \\ M C_{P} - M C_{V} = R \\ C_{P} - C_{V} = \frac{R}{M} \end{aligned}$
For hydrogen $M = 2$
$C_{P} - C_{V} = \frac{R}{2} = a$
For nitrogen $M = 28$
$\begin{aligned} \Rightarrow C_{P} - C_{V} = \frac{R}{28} = b \\ \frac{a}{b} = 14 \end{aligned}$

PHXI13:KINETIC THEORY

360353 For an ideal gas of diatomic molecules

1

C_{P} = \frac{5}{2} R

2

C_{V} = \frac{3}{2} R

3

C_{P} - C_{V} = 2 R

4

C_{P} = \frac{7}{2} R

Explanation:

$C_{P} = (\frac{f}{2} + 1) R = (\frac{5}{2} + 1) R = \frac{7}{2} R$

PHXI13:KINETIC THEORY

360354 Statement A :
The ratio of specific heat of a gas at constant pressure and specific heat at constant volume for a diatomic gas is more than that for a monoatomic gas
Statement B :
The molecules of a monoatomic gas have more degree of freedom than those of a diatomic gas.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both statements are correct.

4 Both Statements are incorrect.

Explanation:

For a monoatomic gas, number of degree of freedom $f = 3$ , and for a diatomic gas, $f = 5$ ,
As, $\frac{C_{P}}{C_{V}} = γ = 1 + \frac{2}{f}$
For monoatomic gas, $\frac{C_{P}}{C_{V}} = \frac{5}{3} = 1.67$ and
For diatomic gas, $\frac{C_{P}}{C_{V}} = \frac{7}{5} = 1.4$
${(\frac{C_{P}}{C_{V}})}_{monoatomic} > {(\frac{C_{P}}{C_{V}})}_{diatomic}$
Both statements are wrong. So option (4) is correct.

PHXI13:KINETIC THEORY

360350 $4.0 g$ of gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is $5.0 J K^{- 1} m o l^{- 1}$ . If the speed of sound in this gas at NTP is $999 m s^{- 1}$ then the specific heat capacity at constant pressure in $J k^{- 1} m o l^{- 1}$ is (Take gas $R = 8.3 J K^{- 1} m o l^{- 1})$

1 8

2 7

3 6.5

4 6

Explanation:

As the given conditions are at NTP $m = M = 4.0 g$
(As it occupies 22.4 liters)
$v_{r m s} = 999 m / s R = 8.3 J \cdot k^{- 1} m o l^{- 1}$
$v_{r m s} = \sqrt{\frac{γ R T}{M}} \Rightarrow γ = \frac{M v^{2}}{R T} = 1.6$
$γ = \frac{C_{P}}{C_{V}} \Rightarrow C_{P} = γ C_{V} = 1.6 \times 5 = 8 J . k^{- 1} m o l^{- 1}$

PHXI13:KINETIC THEORY

360351 If $γ$ is the ratio of specific heats and $R$ is the universal gas constant, then the molar specific heat at constant volume $C_{v}$ is given by

1

\frac{R}{γ - 1}

2

\frac{γ R}{γ - 1}

3

γ R

4

\frac{(γ - 1) R}{γ}

Explanation:

We know that
$\frac{C_{p}}{C_{v}} = γ (1)$
But
$C_{p} - C_{v} = R (2)$
(2)
From (1) & (2)
$γ C_{v} - C_{v} = R \Rightarrow C_{v} = \frac{R}{γ - 1}$

PHXI13:KINETIC THEORY

360352 $C_{P}$ and $C_{V}$ are specific heats at constant pressure and constant volume respectively. It is observed that $C_{p} - C_{v} = a$ for hydrogen gas $C_{p} - C_{v} = b$ for nitrogen gas. The correct relation between $a$ and $b$ :

1

a = 14 b

2

a = 28 b

3

a = \frac{1}{14} b

4

a = b

Explanation:

Molar specific heat $C^{'} = \frac{Δ Q}{n Δ T}$
Specific heat $C = \frac{Δ Q}{m Δ T}$
$\begin{aligned} \frac{C^{'}}{C} = \frac{m}{n} = M (Molecular weight) \\ C = \frac{C^{'}}{M} \\ C_{P}^{'} - C_{V}^{'} = R \\ M C_{P} - M C_{V} = R \\ C_{P} - C_{V} = \frac{R}{M} \end{aligned}$
For hydrogen $M = 2$
$C_{P} - C_{V} = \frac{R}{2} = a$
For nitrogen $M = 28$
$\begin{aligned} \Rightarrow C_{P} - C_{V} = \frac{R}{28} = b \\ \frac{a}{b} = 14 \end{aligned}$

PHXI13:KINETIC THEORY

360353 For an ideal gas of diatomic molecules

1

C_{P} = \frac{5}{2} R

2

C_{V} = \frac{3}{2} R

3

C_{P} - C_{V} = 2 R

4

C_{P} = \frac{7}{2} R

Explanation:

$C_{P} = (\frac{f}{2} + 1) R = (\frac{5}{2} + 1) R = \frac{7}{2} R$

PHXI13:KINETIC THEORY

360354 Statement A :
The ratio of specific heat of a gas at constant pressure and specific heat at constant volume for a diatomic gas is more than that for a monoatomic gas
Statement B :
The molecules of a monoatomic gas have more degree of freedom than those of a diatomic gas.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both statements are correct.

4 Both Statements are incorrect.

Explanation:

For a monoatomic gas, number of degree of freedom $f = 3$ , and for a diatomic gas, $f = 5$ ,
As, $\frac{C_{P}}{C_{V}} = γ = 1 + \frac{2}{f}$
For monoatomic gas, $\frac{C_{P}}{C_{V}} = \frac{5}{3} = 1.67$ and
For diatomic gas, $\frac{C_{P}}{C_{V}} = \frac{7}{5} = 1.4$
${(\frac{C_{P}}{C_{V}})}_{monoatomic} > {(\frac{C_{P}}{C_{V}})}_{diatomic}$
Both statements are wrong. So option (4) is correct.