Thermodynamics Questions along with solutions (Questions for IITJEE)

Question 1:A gas is contained in a vertical, frictionless piston cylinder device. The piston has a mass of 20 kg with a cross-sectional area of 20 cm² and is pulled with a force of 100N. If the atmospheric pressure is 100 kPa, determine the pressure inside.


Question 2:A piston-cylinder device has a ring to limit the expansion stroke. Initially the mass of Oxygen is 2 kg at 500 kPa, 30° C. Heat is now transferred until the piston touches the stop, at which point the volume is twice the original volume. More heat is transferred until the pressure inside also doubles. Determine the amount of heat transfer and the final temperature.


Question 3: A piston cylinder device contains 1 kg of oxygen at 150 kPa, 30°C. The cross-sectional area of the piston is 0.1 m². Heat is now added causing gas to expand. When the volume reaches 0.2 m³, the piston reaches a linear spring with a spring constant of 120 kN/m. More heat is added until the piston rises another 25 cm. Determine the final pressure, temperature and the energy transfers.


Question 4:Is the energy of the system U an intensive or extensive variable?



Question 5:Suppose we have M+N systems prepared, and the first is in thermal equilibrium with the second, the second in thermal equilibrium with the third, etc., until system M+N- 1 is in thermal equilibrium with the M+Nth system. Is the first system in thermal equilibrium with the M+Nth?


Question 6:A gas is contained in a cylinder with a moveable piston on which a heavy block is placed. Suppose the region outside the chamber is evacuated and the total mass of the block and the movable piston is 102 kg. When 2140 J of heat flows into the gas, the internal energy of the gas increases by 1580 J. What is the distance s through which the piston rises?


Question 7:A resistance thermometer is such that resistance varies with temperature as
R_T=R₀(1+aT+bT⁵)
where T represent Temperature on Celsius scale And a,b,R₀ are constants.R₀ unit is ohm
Based on above data ,Find out the unit of a,b


Solutions

Please take a look at other Thermal post
Thermal Expansion
Study Tips Part 1
Study Tips Part 2
Thermo Quick Recap
Conceptual Questions Part 1
Conceptual Questions Part 2
Conceptual Questions Part 3
Conceptual Questions Part 4
IITJEE Objective Questions part 1
IITJEE Objective Questions Part 2
Thermal Expansion Problems
IITJEE Subjective Questions
Thermo Questions

Second derivatives of vector fields and product rules

There are number of rules that we might use while solving problems involving vector differentiation. These are

1.Sum rule





2. Multiplication by a constant





3. Product rule

fig3

4. Quotient rule

fig4

5.

Semiconductor Physics (Things you should know)

1. Resistance of a pure semiconductor is millions and millions of times greater then that of a good conductor like copper.
2 Charge carriers in semiconductors are electrons(-e) and holes(p having charge equal to +e).
3 Pure semiconductor known as intrinsic semiconductor contains equal number of both holes and electrons.
4 Drift velocity of electrons is greater then that of holes.
5 Taking both charge carriers in semiconductor into account current is given as I=neA(v_n+v_p) where n is number of holes and electrons, v_n is the drift velocity of electrons and v_p is drift velocity of holes and A is the cross-sectional area.
6 Electrical resistance of pure semiconducter decreases with increase in temperature.
7 Semiconductors can be doped with a tiny amount of impurity such as one part in a million to form an impure or extrinsic semiconductor.
8 p-type semiconductor is a type of ectrinsic semiconductor formed when pure semiconductor is doped with trivalent element (for ex- indium). It has large majority of holes and small minority of electrons. Thus majority charge carriers in a p-type semiconductor are holes.
9 n-type semiconductor is a type of ectrinsic semiconductor formed when pure semiconductor is doped with pentavalent element (for ex- phosphorus). It has large majority of electrons and small minority of holes. Thus majority charge carriers in a p-type semiconductor are electrons.
10 Junction diode is a simplest kind of semiconductor device. It has a pn junction and consists of a p-type crystal and n-type crystal and is formed by growing n-type semiconductor over p-type semiconductor. Junction diodes are used as rectifiers.
11 Bipolar junction transistor is a three terminal device. There are two type of transistors npn and pnp transistor. Three terminals of the transistor are joined to base, emitter and collector of the transistor.
12 With Common emitter transistor, the base current I_b is the input current and the

Gravitation questions for IITJEE

1.Which is of the following statement is true
A) Gravitational constant G value does not depend on the medium between the bodies
B) Gravitational constant G depends on the masses of the bodies and the sizes of the bodies
a A & B both are correct
b only A is correct
c Only B is correcr
d A and B both are wrong

2.If the distance between the earth and sun were half its present value,the number of days in a year would be
a. 64.5
b. 129
c. 182.5
d. 730

3.if both the mass of earth and its radius are decreased by 1%,the value of acceleration of gravity will
a. Decrease by 1%
b Increase by 1%
c. Increase by 2%
d remain unchanged

4. A body weigh W newton of the surface of the earth.Its weight at a height equal to half the radius of the earth will be
a. W/2
b. 2W/3
c. 4W/9
d. W/4

5.when a stone of mass m is falling in th earth of mass M,the acceleration of the earth will be
a zero
b. mg/M
c. Mg/m
d g

6.The weight of the object will be
a. zero at the center of the earth
b.same in all the satellites
c. same at all the points on the surface of the earth
d. none of the above

7.Which is of the following statement is true
A) it is possible to put an artificial satellite in a orbit such a way that it will remain always directly over New Delhi
B) An earth satellite continues to move in the orbit due to centripetal force provided by the burning of the fuel of its engine
a A & B both are correct
b only A is correct
c Only B is correcr
d A and B both are wrong


8. A mass m is divided into two part ym and (1-y)m .For a given seperation,the value of y for which the gravitattional attraction between the two pieces becomes maximum
a. 1/2
b. 3/5
c. 1
d 2

9.Two bodies of mass M and 2M are at rest at infinte seperation.They move towards each other under the mutual gravitaional attraction.Then at seperation r ,which of the following is false
a. The total energy of the system is not zero
b The force between them is zero
c. The center of the mass of the system is movind
d non of the above

10.Choose the correct statement
a. the gravitational forces between the two bodies are an action and reaction pair
b. G and g are constant everywhere
c.The acceleration due to gravity increase due to rotation of the earth
d. none of the above


Solutions

String, pully and spring

A lot of problems in mechanics involves string, pulley and springs for example masses are attached to string or spring and so on. Here are some concepts you need to remember while solving problems involving string, spring and pulleys.
(1) String
A. If not staded in the question consider the string to be inextensible.
B. Different blocks connected to an inextensible string would have same acceleration and for extensible string blocks would have different acceleration until the string can stretch.
C. Unless otherwise specified consider the string to be light i.e., consider its mass to be negligible in comparison to the block connected to it.
D. For a massless string tension in the string is zero although an ideal massless string is an practical impossibility.
E. Tension on different parts of the string would be different if string possess a considerable mass.

(2) Pulley
A. Unless or otherwise specified consider the pulley to be light having no effect on the system due to its weight.
B. The tension on strion on either side of pulley is taken to be same
C. If not specified consider the oulley to be frictionless in nature.

(3) Spring
A. Unless or otherwise specified consider the spring to be light and force constant of spring is same throughout whole length of the spring.
B. Spring has a elastic property that it can be compressed and stretched easily.
C. To stretch or compress a spring equal and opposite forces have to be applied at both the ends of the spring and in responce spring apply equal and opposite restoring force to bring the spring back to its natural position.
D For small compression and elongations this restoring force is given by Hook's Law which is
F=kx
where k is the spring constant and x is elongation or compression from the natural length of the spring.

So keep solving more and more physics problems Keeping these facts in mind. All the very best for your exams.

IITJEE Tips and Tricks

Solve Force and motion problems easily
(1) First read the problem carefully.
(2) Determine which type of force is exerted in the system and where it is exertwd.
(3) See whether Newton's law of motion are applicable for the particular system or not i.e., see wherher frame of referance you are working with is inertial or non-inertial frame of refrence.
(4) Determine the system of units you have to use to solve a problem. If physical quantities in the question are given in different units then convert them to a convinent unit you want to work with generally S.I. system of unit is used in our text books.
(5) See if frictional forces are acting on the system if yes then take them into account.
(6) While taking care of friction forces see if they are static or kinetic in nature and accordingly work with them.
(6) Look for the direction of the frictional forces.
So keeping these simple points in mind you can solve force and motion problems easily

Physics pocket diary of concepts and formulas

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All the best for your Exams.