Heat and Thermodynamics — Page 4 | JEE Physics

Q31

1 mole of a gas with

\gamma = 7/5

is mixed with

1

mole of a gas with

\gamma = 5/3,

then the value of

\gamma

for the resulting mixture is

A

7/5

B

2/5

C

3/2

D

12/7

Correct Answer

Option C

Solution

If

{n_1}

moles of adiabatic exponent

{\gamma _1}

is mixed with

{n_2}

moles of adiabatic exponent

{\gamma _2}

then the adiabatic component of the resulting mixture is given by

{{{n_1} + {n_2}} \over {\gamma - 1}} = {{{n_1}} \over {{\gamma _1} - 1}} + {{{n_2}} \over {{\gamma _2} - 1}}

{{1 + 1} \over {\gamma - 1}} = {1 \over {{7 \over 5} - 1}} + {1 \over {{5 \over 3} - 1}}

$\therefore$

{2 \over {\gamma - 1}} = {5 \over 2} + {3 \over 2} = 4

$\therefore$

2 = 4\gamma - 4 \Rightarrow \gamma = {6 \over 4} = {3 \over 2}

Q32

Two spheres of the same material have radii

1

m

and

4

m

and temperatures

4000

K

and

2000

K

respectively. The ratio of the energy radiated per second by the first sphere to that by the second is

A

1:1

B

16:1

C

4:1

D

1:9

Correct Answer

Option A

Solution

The energy radiated per second is given by

E = e\sigma {T^4}A

For same material

e

is same. $\sigma$ is stefan's constant $\therefore$

{{{E_1}} \over {{E_2}}} = {{T_1^4{A_1}} \over {T_2^4{A_2}}} = {{T_1^44\pi r_1^2} \over {T_2^44\pi r_2^2}}

= {{{{\left( {4000} \right)}^4} \times {1^2}} \over {{{\left( {2000} \right)}^4} \times {4^2}}} = {1 \over 1}

Q33

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio

{C_p}/{C_V}

for the gas is

A

{4 \over 3}

B

2

C

{5 \over 3}

D

{3 \over 2}

Correct Answer

Option D

Solution

P \propto {T^3} \Rightarrow P{T^{ - 3}} =

constant ....

(i)

But for an adiabatic process, the pressure temperature relationship is given by

{P^{1 - \gamma }}\,\,{T^\gamma } =

constant

\Rightarrow P{T^{{\gamma \over {1 - \gamma }}}} =

constant. ....

(ii)

From

(i)

and

(ii)

{\gamma \over {1 - \gamma }} = - 3 \Rightarrow \gamma = - 3 + 3\gamma \Rightarrow \gamma = {3 \over 2}

Q34

The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by

A Rayleigh Jeans law

B Planck's law of radiation

C Stefan's law of radiation

D Wien's law

Correct Answer

Option D

Solution

Wein's law correctly explanations the spectrum

Q35

A carnot engine takes

3 \times {10^6}

cal. of heat from a reservoir at

{627^ \circ }C,

and gives it to a sink at

{27^ \circ }C

. The work done by the engine is

A

4.2 \times {10^6}J

B

8.4 \times {10^6}J

C

16.8 \times {10^6}J

D zero

Correct Answer

Option B

Solution

\eta = 1 - {{{T_2}} \over {{T_1}}}

= 1 - {{\left( {273 + 27} \right)} \over {\left( {273 + 627} \right)}}

= 1 - {{300} \over {900}}

= 1 - {1 \over 3} = {2 \over 3}

But

\eta = {W \over Q}

$\therefore$

{W \over Q} = {2 \over 3} \Rightarrow W

= {2 \over 3} \times Q

= {2 \over 3} \times 3 \times {10^6}

= 2 \times {10^6}cal

= 2 \times {10^6} \times 4.2\,J

= 8.4 \times {10^6}J

Q36

Which of the following parameters does not characterize the thermodynamic state of mattter?

A Temperature

B Pressure

C Work

D Volume

Correct Answer

Option C

Solution

Work is a path function. The remaining three parameters are state function.

Q37

The rms speeds of the molecules of Hydrogen, Oxygen and Carbon dioxide at the same temperature are VH, VO and VC respectively then :

A VH > VO > VC

B VC > VO > VH

C VH = VO > VC

D VH = VO = VC

Correct Answer

Option A

Solution

{V_{RMS}} = \sqrt {{{3RT} \over {{M_W}}}}

At the same temperature

{V_{RMS}} \propto {1 \over {\sqrt {{M_W}} }}

$\Rightarrow$ VH > VO > VC Option (a)

Q38

Heat given to a body which raises its temperature by

{1^ \circ }C

is

A water equivalent

B thermal capacity

C specific heat

D temperature gradient

Correct Answer

Option B

Solution

Heat required for raising the temperature of the whole body by

{1^ \circ }C

is called the thermal capacity of the body.

Q39

Which of the following is more close to a black body?

A black board paint

B green leaves

C black holes

D red roses

Correct Answer

Option A

Solution

Black board paint is quite approximately equal to black bodies.

Q40

If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

A increase

B remain unchanged

C decrease

D first increase then decrease

Correct Answer

Option C

Solution

When water is cooled to form ice, energy is released from water in the form of heat.

As energy is equivalent to mass therefore when water is cooled to ice, its mass decreases.