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In which part , air and gas(petrol) mixes in internal combustion engine?

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Important Questions on Sets, Relations and Functions

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

A heat engine is involved with exchange of heat of

1915 J, - 40 J, + 125 J

and

- Q J

, during one cycle achieving and efficiency of

50.0 %

. The value of

Q

is:

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

For which of the following processes, entropy change is zero?

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

A Carnot engine operates between two reservoirs of temperatures

900 K

and

300 K

. The engine performs

1200 J

of work per cycle. The heat energy (in

J

) delivered by the engine to the low temperature reservoir, in a cycle, is _____________

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

A carnot engine working between

27 ° C

and

127 ° C,

draws

600 J

of heat from the reservoir in one cycle. The work done by the engine

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

Consider a two stage Carnot engine. In the first stage heat

Q_{1}

is absorbed at temperature

T

and heat

Q_{2}

is expelled at temperature

α T

(where

α < 1

). In the second stage heat

Q_{2}

is absorbed at temperature

α T

and heat

Q_{3}

is expelled at temperature

β T (β < α) .

The efficiency of the Carnot engine will be

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

Consider an engine that absorbs

130 cal

of heat from a hot reservoir and delivers

30 cal

heat to a cold reservoir in each cycle. The engine also consumes

2 J

energy in each cycle to overcome friction. If the engine works at

90

cycles per minute, what will be the maximum power delivered to the load? [Assume the thermal equivalent of heat is

4.2 J / cal

]

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

A car engine has a power of

20 kW

. The car makes a roundtrip of 1 hour. If the thermal efficiency of the engine is

40 %

and the ambient temperature is

300 K

. The energy generated by fuel combustion is

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

A Carnot's engine working between

400 K

and

800 K

has a work output of

1200 J

per cycle. The amount of heat energy supplied to the engine from the source in each cycle is:

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

The carnot heat engine have an efficiency of

50 % .

The temperature of sink is maintained at

500 K .

To increase the efficiency upto

80 %,

the increment in the source temperature is

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

What will be the efficiency of a Carnot engine if it takes heat from reservoir, at

100 ° C

and rejects heat to a sink at,

50 ° C

HARD

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

A solid body of constant heat capacity

1 J {(℃)}^{- 1}

is being heated by keeping it in contact with reservoirs in two ways: (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies the same amount of heat. (ii) Sequentially keeping in contact with

8

reservoirs such that each reservoir supplies the same amount of heat. In both, cases the body is brought from initial temperature

100 K

to final temperature

200 K

. Entropy change of the body in the two cases respectively is: Note: This question was awarded as a bonus since temperatures were given in centigrade instead of in Kelvin. Proper corrections are made in the question to avoid it.

HARD

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

Graphs below show the entropy versus energy $U$ of two systems $1$ and $2$ at constant volume. The initial energies of the systems are indicated by $U_{1, i}$ and $U_{2, i},$ respectively. Graphs are drawn to the same scale. The systems are then brought into thermal contact with each other. Assume that, at all times the combined energy of the two systems remains constant. Choose the most appropriate option indicating the energies of the two systems and the total entropy after they achieve the equilibrium.

Question Image

HARD

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

The efficiency of the cycle shown below in the figure (consisting of one isobar, one adiabat and one isotherm) is $50 % .$ The ratio, $x,$ between the highest and lowest temperatures attained in this cycle obeys (the working substance is a ideal gas):-

Question Image

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to

Question Image

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by

52 K,

its efficiency is doubled. The temperature in Kelvin of the source will be ___ .

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

A heat engine has an efficiency of

\frac{1}{6}

. When the temperature of sink is reduced by

62 ° C

, its efficiency get doubled. The temperature of the source is :

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

For an ideal heat engine, the temperature of the source is

127 ° C

. In order to have

60 %

efficiency the temperature of the sink should be __________

{}^{\circ}C

. (Round off to the nearest integer)

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

By leaving the door of a small standard domestic refrigerator open, it is not possible to cool a room, because it violates the ______

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

Entropy of the universe tends to be

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

One mole of an ideal monatomic gas undergoes the following four reversible processes:
Step

1 :

It is first compressed adiabatically from volume

V_{1}

1 m^{2} .

Step

2 :

then expanded isothermally to volume

10 m^{3}

Step

3 :

then expanded adiabatically to volume

V_{3}

Step

4 :

then compressed isothermally to volume

V_{1} .

If the efficiency of the above cycle is

\frac{3}{4}

then

V_{1}

In which part , air and gas(petrol) mixes in internal combustion engine?

Important Questions on Sets, Relations and Functions

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