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The molar heat capacity of oxygen gas at STP is nearly 2.5R. As the temperature is increased, it gradually increases and approaches 3.5 R. The most appropriate reason for this behaviour is that at high temperature

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Important Questions on Thermodynamics

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

Consider two ideal diatomic gases

A

and

B

at some temperature

T

. Molecules of the gas

A

are rigid, and have a mass

m

. Molecules of the gas

B

have an additional vibrational mode and have a mass

\frac{m}{4}

. The ratio of the specific heats

{(C_{V}^{})}_{A} and {(C_{V}^{})}_{B}

of gas

A

and

B,

respectively is:

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

The specific heats,

C_{p}

and

C_{v}

of a gas of diatomic molecules,

A,

are given (in units of

J m o l^{- 1} K^{- 1}

) by

29

and

22,

respectively. Another gas of diatomic molecules,

B,

has the corresponding values

30

and

21 .

If they are treated as ideal gases, then:

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

Two moles of an ideal gas, with

\frac{C_{P}}{C_{V}} = \frac{5}{3}

, are mixed with three moles of another ideal gas

\frac{C_{P}}{C_{V}} = \frac{4}{3}

. The value of

\frac{C_{P}}{C_{V}}

for the mixture is

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

What will be the molar specific heat at constant volume of an ideal gas consisting of rigid diatomic molecules?

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

For a rigid diatomic molecule, the universal gas constant

R = n C_{P}

, where,

C_{P}

is the molar specific heat at constant pressure and

n

is a number. Hence,

n

is equal to

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

The values of

C_{p}

and

C_{v}

for a diatomic gas are respectively

(R = g a s

constant)

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

Consider a mixture of

n

moles of helium gas and

2 n

moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its

\frac{C_{P}}{C_{V}}

value will be:

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

The correct relation between the degrees of freedom

f

and the ratio of specific heat

γ

is:

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

An ideal gas has molecules with

5

degrees of freedom. The ratio of specific heats at constant pressure

(C_{p})

and at constant volume

(C_{V})

is:

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

When heat

Q

is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by

∆ T

. The heat required to produce the same change in temperature, at a constant pressure is:

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

One mole of a monoatomic ideal gas undergoes a quasistatic process, which is depicted by a straight line joining points

(V_{0}, T_{0})

and

(2 V_{0}, 3 T_{0})

in a

V - T

diagram. What is the value of the heat capacity of the gas at the point

(V_{0}, T_{0}) ?

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

For a diatomic ideal gas in a closed system, which of the following plots does not correctly describe the relation between various thermodynamic quantities?

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

One gram mole of an ideal gas

A

with the ratio of constant pressure and constant volume specific heats

γ_{A} = \frac{5}{3}

is mixed with

n

gram moles of another ideal gas

B

with

γ_{B} = \frac{7}{5}

. If the

γ

for the mixture is

\frac{19}{13}

, then what will be the value of

n

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

One mole of

O_{2}

gas is heated at constant pressure starting at

27 ° C

. How much energy must be added to the gas as heat to double its volume?

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

The ratio of

\frac{C_{p}}{C_{v}}

for a diatomic gas is

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

For a gas

C_{P} - C_{V} = R

in a state

P

and

C_{P} - C_{V} = 1.10 R

in a state

Q, T_{P}

and

T_{Q}

are the temperatures in two different states

P

and

Q

, respectively. Then

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

Two different metal bodies $A$ and $B$ of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is:

Question Image

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

A cylinder with fixed capacity of

67.2

litre contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by

20 ° C

is:
[Given that

R = 8.31 J m o l^{- 1} K^{- 1}]

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

C_{p} - C_{v} = \frac{R}{M}

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 and

C_{p} - C_{v} = b

for nitrogen gas. The correct relation between

a

and

b

is:

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Specific Heat Capacity of Gases

4.0 g

of a gas occupies

22.4

liters 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

952 m s^{- 1}

, then the heat capacity at constant pressure is

(Take gas constant

R = 8.3 J K^{- 1} m o l^{- 1}

)

The molar heat capacity of oxygen gas at STP is nearly 2.5R. As the temperature is increased, it gradually increases and approaches 3.5 R. The most appropriate reason for this behaviour is that at high temperature

Important Questions on Thermodynamics

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