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Kinetic Theory of Gases

139023 Let speed of sound at $0^{0} C$ be $332 {ms}^{- 1}$ . On a winter day sound travels $342 {ms}^{- 1}$ in one second. The atmospheric temperature on that day is:

1

{7.0}^{\circ} C

2

{16.7}^{\circ} C

3

{12.5}^{\circ} C

4

{10.9}^{\circ} C

Explanation:

B Given that,
$T_{1} = 0^{\circ} C = 273 K, v_{1} = 332 m / \sec$
$T_{2} = ?, v_{2} = 342 m / \sec$
We know that,
$v = \sqrt{\frac{γ RT}{M}}$
$V \propto \sqrt{T}$
$\frac{v_{1}}{v_{2}} = \sqrt{\frac{T_{1}}{T_{2}}}$
$\frac{332}{342} = \sqrt{\frac{273}{T_{2}}}$
$T_{2} = \frac{273 \times 342 \times 342}{332 \times 332}$
$T_{2} = 289.7 K$
$T_{2} = (289.7 - 273)$
$T_{2} = {16.7}^{\circ} C$

Assam CEE-2017

Kinetic Theory of Gases

139024 If pressure and temperature of an ideal gas are doubled and volume is halved, the number of molecules of gas

1 Becomes half

2 Becomes two times

3 Becomes four times

4 Remain constant

Explanation:

A From ideal gas equation,
$PV = nRT$
$n = \frac{PV}{RT}$
It is given as pressure and temperature of the ideal gas is doubled and Volume of the ideal gas is halved
$P = 2 P, V = \frac{V}{2} and T = 2 T$
$2 P \times \frac{V}{2} = nRT \times 2$
$P \times V = nRT \times 2$
$n = \frac{PV}{2 \times RT}$
From this it is clear that, number of molecules or moles is halved when the pressure and temperature are double and volume is halved.

JCECE-2017

Kinetic Theory of Gases

139025 p-V diagram of an ideal gas is shown. The gas undergoes from initial state $A$ to final state $B$ such that initial and final volumes are same. Select the correct alternative for given process AB.

1 Work done by gas is positive

2 Work done by gas is negative

3 Temperature of gas increases continuously

4 Process is isochoric

UPSEE - 2017

Kinetic Theory of Gases

139026 If the pressure and the volume of certain quantity of ideal gas are halved, then its temperature

1 is doubled

2 becomes one-fourth

3 remains constant

4 is halved

5 become four times

Explanation:

B The equation for an ideal gas is given by-
$PV = nRT$
Here, the pressure and volume of certain quantity is getting halved,
$∴ \frac{P}{2} \times \frac{V}{2} = {nRT}^{'}$
$\frac{PV}{4} = {nRT}^{'}$
From equation (i),
$\frac{nRT}{4} = {nRT}^{'}$
$T^{'} = \frac{T}{4}$
Hence, the temperature of ideal gas becomes one fourth.

Kerala CEE 2012

Kinetic Theory of Gases

139023 Let speed of sound at $0^{0} C$ be $332 {ms}^{- 1}$ . On a winter day sound travels $342 {ms}^{- 1}$ in one second. The atmospheric temperature on that day is:

1

{7.0}^{\circ} C

2

{16.7}^{\circ} C

3

{12.5}^{\circ} C

4

{10.9}^{\circ} C

Explanation:

B Given that,
$T_{1} = 0^{\circ} C = 273 K, v_{1} = 332 m / \sec$
$T_{2} = ?, v_{2} = 342 m / \sec$
We know that,
$v = \sqrt{\frac{γ RT}{M}}$
$V \propto \sqrt{T}$
$\frac{v_{1}}{v_{2}} = \sqrt{\frac{T_{1}}{T_{2}}}$
$\frac{332}{342} = \sqrt{\frac{273}{T_{2}}}$
$T_{2} = \frac{273 \times 342 \times 342}{332 \times 332}$
$T_{2} = 289.7 K$
$T_{2} = (289.7 - 273)$
$T_{2} = {16.7}^{\circ} C$

Assam CEE-2017

Kinetic Theory of Gases

139024 If pressure and temperature of an ideal gas are doubled and volume is halved, the number of molecules of gas

1 Becomes half

2 Becomes two times

3 Becomes four times

4 Remain constant

Explanation:

A From ideal gas equation,
$PV = nRT$
$n = \frac{PV}{RT}$
It is given as pressure and temperature of the ideal gas is doubled and Volume of the ideal gas is halved
$P = 2 P, V = \frac{V}{2} and T = 2 T$
$2 P \times \frac{V}{2} = nRT \times 2$
$P \times V = nRT \times 2$
$n = \frac{PV}{2 \times RT}$
From this it is clear that, number of molecules or moles is halved when the pressure and temperature are double and volume is halved.

JCECE-2017

Kinetic Theory of Gases

139025 p-V diagram of an ideal gas is shown. The gas undergoes from initial state $A$ to final state $B$ such that initial and final volumes are same. Select the correct alternative for given process AB.

1 Work done by gas is positive

2 Work done by gas is negative

3 Temperature of gas increases continuously

4 Process is isochoric

UPSEE - 2017

Kinetic Theory of Gases

139026 If the pressure and the volume of certain quantity of ideal gas are halved, then its temperature

1 is doubled

2 becomes one-fourth

3 remains constant

4 is halved

5 become four times

Explanation:

B The equation for an ideal gas is given by-
$PV = nRT$
Here, the pressure and volume of certain quantity is getting halved,
$∴ \frac{P}{2} \times \frac{V}{2} = {nRT}^{'}$
$\frac{PV}{4} = {nRT}^{'}$
From equation (i),
$\frac{nRT}{4} = {nRT}^{'}$
$T^{'} = \frac{T}{4}$
Hence, the temperature of ideal gas becomes one fourth.

Kerala CEE 2012

Kinetic Theory of Gases

139023 Let speed of sound at $0^{0} C$ be $332 {ms}^{- 1}$ . On a winter day sound travels $342 {ms}^{- 1}$ in one second. The atmospheric temperature on that day is:

1

{7.0}^{\circ} C

2

{16.7}^{\circ} C

3

{12.5}^{\circ} C

4

{10.9}^{\circ} C

Explanation:

B Given that,
$T_{1} = 0^{\circ} C = 273 K, v_{1} = 332 m / \sec$
$T_{2} = ?, v_{2} = 342 m / \sec$
We know that,
$v = \sqrt{\frac{γ RT}{M}}$
$V \propto \sqrt{T}$
$\frac{v_{1}}{v_{2}} = \sqrt{\frac{T_{1}}{T_{2}}}$
$\frac{332}{342} = \sqrt{\frac{273}{T_{2}}}$
$T_{2} = \frac{273 \times 342 \times 342}{332 \times 332}$
$T_{2} = 289.7 K$
$T_{2} = (289.7 - 273)$
$T_{2} = {16.7}^{\circ} C$

Assam CEE-2017

Kinetic Theory of Gases

139024 If pressure and temperature of an ideal gas are doubled and volume is halved, the number of molecules of gas

1 Becomes half

2 Becomes two times

3 Becomes four times

4 Remain constant

Explanation:

A From ideal gas equation,
$PV = nRT$
$n = \frac{PV}{RT}$
It is given as pressure and temperature of the ideal gas is doubled and Volume of the ideal gas is halved
$P = 2 P, V = \frac{V}{2} and T = 2 T$
$2 P \times \frac{V}{2} = nRT \times 2$
$P \times V = nRT \times 2$
$n = \frac{PV}{2 \times RT}$
From this it is clear that, number of molecules or moles is halved when the pressure and temperature are double and volume is halved.

JCECE-2017

Kinetic Theory of Gases

139025 p-V diagram of an ideal gas is shown. The gas undergoes from initial state $A$ to final state $B$ such that initial and final volumes are same. Select the correct alternative for given process AB.

1 Work done by gas is positive

2 Work done by gas is negative

3 Temperature of gas increases continuously

4 Process is isochoric

UPSEE - 2017

Kinetic Theory of Gases

139026 If the pressure and the volume of certain quantity of ideal gas are halved, then its temperature

1 is doubled

2 becomes one-fourth

3 remains constant

4 is halved

5 become four times

Explanation:

B The equation for an ideal gas is given by-
$PV = nRT$
Here, the pressure and volume of certain quantity is getting halved,
$∴ \frac{P}{2} \times \frac{V}{2} = {nRT}^{'}$
$\frac{PV}{4} = {nRT}^{'}$
From equation (i),
$\frac{nRT}{4} = {nRT}^{'}$
$T^{'} = \frac{T}{4}$
Hence, the temperature of ideal gas becomes one fourth.

Kerala CEE 2012

Kinetic Theory of Gases

139023 Let speed of sound at $0^{0} C$ be $332 {ms}^{- 1}$ . On a winter day sound travels $342 {ms}^{- 1}$ in one second. The atmospheric temperature on that day is:

1

{7.0}^{\circ} C

2

{16.7}^{\circ} C

3

{12.5}^{\circ} C

4

{10.9}^{\circ} C

Explanation:

B Given that,
$T_{1} = 0^{\circ} C = 273 K, v_{1} = 332 m / \sec$
$T_{2} = ?, v_{2} = 342 m / \sec$
We know that,
$v = \sqrt{\frac{γ RT}{M}}$
$V \propto \sqrt{T}$
$\frac{v_{1}}{v_{2}} = \sqrt{\frac{T_{1}}{T_{2}}}$
$\frac{332}{342} = \sqrt{\frac{273}{T_{2}}}$
$T_{2} = \frac{273 \times 342 \times 342}{332 \times 332}$
$T_{2} = 289.7 K$
$T_{2} = (289.7 - 273)$
$T_{2} = {16.7}^{\circ} C$

Assam CEE-2017

Kinetic Theory of Gases

139024 If pressure and temperature of an ideal gas are doubled and volume is halved, the number of molecules of gas

1 Becomes half

2 Becomes two times

3 Becomes four times

4 Remain constant

Explanation:

A From ideal gas equation,
$PV = nRT$
$n = \frac{PV}{RT}$
It is given as pressure and temperature of the ideal gas is doubled and Volume of the ideal gas is halved
$P = 2 P, V = \frac{V}{2} and T = 2 T$
$2 P \times \frac{V}{2} = nRT \times 2$
$P \times V = nRT \times 2$
$n = \frac{PV}{2 \times RT}$
From this it is clear that, number of molecules or moles is halved when the pressure and temperature are double and volume is halved.

JCECE-2017

Kinetic Theory of Gases

139025 p-V diagram of an ideal gas is shown. The gas undergoes from initial state $A$ to final state $B$ such that initial and final volumes are same. Select the correct alternative for given process AB.

1 Work done by gas is positive

2 Work done by gas is negative

3 Temperature of gas increases continuously

4 Process is isochoric

UPSEE - 2017

Kinetic Theory of Gases

139026 If the pressure and the volume of certain quantity of ideal gas are halved, then its temperature

1 is doubled

2 becomes one-fourth

3 remains constant

4 is halved

5 become four times

Explanation:

B The equation for an ideal gas is given by-
$PV = nRT$
Here, the pressure and volume of certain quantity is getting halved,
$∴ \frac{P}{2} \times \frac{V}{2} = {nRT}^{'}$
$\frac{PV}{4} = {nRT}^{'}$
From equation (i),
$\frac{nRT}{4} = {nRT}^{'}$
$T^{'} = \frac{T}{4}$
Hence, the temperature of ideal gas becomes one fourth.

Kerala CEE 2012

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