Match the following: (where R is gas constant) Column I Column II (a) Molar specific heat of helium gas at constant volume (i) 3 R (b) Molar specific heat of oxygen at constant volume (ii) 3 . 5 R (c) Molar specific heat of carbon dioxide at constant volume (iii) 1 . 5 R (d) Molar specific heat of hydrogen at constant pressure (iv) 2 . 5 R

( a - iii ) , ( b - iv ) , ( c - i ) , ( d - ii )

( a - i ) , ( b - ii ) , ( c - iii ) , ( d - iv )

( a - ii ) , ( b - ii ) , ( c - iv ) , ( d - i )

( a - iv ) , ( b - i ) , ( c - ii ) , ( d - iii )

EASY

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$2$ moles of helium gas is mixed with $3$ moles of hydrogen molecules (taken to be rigid). Find the molar specific heat of the mixture at constant volume. $(R = 8.3 J / mol K)$

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Important Questions on Thermodynamics

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

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}) ?

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

The values of

C_{p}

and

C_{v}

for a diatomic gas are respectively

(R = g a s

constant)

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

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>Heat Capacity

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>Heat Capacity

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

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

The ratio of

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

for a diatomic gas is

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

The quantities of heat required to raise the temperature of two solid copper spheres of radii

r_{1}

and

r_{2} (r_{1} = 1.5 r_{2})

through

1 K

are in the ratio:

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

An ideal gas undergoes a four step cycle as shown in the $P - V$ diagram below. During this cycle, heat is absorbed by the gas in:

Question Image

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

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}]

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

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:

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

For a monoatomic ideal gas following the cyclic process $A B C A$ shown in the $U$ vs $ρ$ plot, identify the incorrect option:

Question Image

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

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}

)

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

Match the following: (where $R$ is gas constant)

	Column I		Column II
(a)	Molar specific heat of helium gas at constant volume	(i)	$3 R$
(b)	Molar specific heat of oxygen at constant volume	(ii)	$3.5 R$
(c)	Molar specific heat of carbon dioxide at constant volume	(iii)	$1.5 R$
(d)	Molar specific heat of hydrogen at constant pressure	(iv)	$2.5 R$

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

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>Heat Capacity

For a gas if

γ = 1.4,

then atomicity, specific heat capacity at constant pressure and specific heat capacity at constant volume of the gas are respectively

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

A metal cube absorbs

2100.0 J

of heat when its temperature is raised by

2 ° C

. If the specific heat of the metal is

900 J {kg}^{- 1} K^{- 1}

, then the mass of the cube is

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

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?

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

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:

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Heat Capacity

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:

2 moles of helium gas is mixed with 3 moles of hydrogen molecules (taken to be rigid). Find the molar specific heat of the mixture at constant volume.(R = 8.3 J/mol K)

Important Questions on Thermodynamics

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$2$ moles of helium gas is mixed with $3$ moles of hydrogen molecules (taken to be rigid). Find the molar specific heat of the mixture at constant volume. $(R = 8.3 J / mol K)$