Case study (4 Marks)

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Question 14 Marks

The number of independent ways by which a dynamic system can move, without violating any constraint imposed on it, is called the number of degrees of freedom. According to the law of equipartition of energy, for any dynamic system in thermal equilibrium, the total energy for the system is equally divided among the degree of freedom.

1. If gas has $n$ degree of freedom, the ratio of specific heat is:
(a) $-2 n$ (b) 2 n (c) $1+2 / n$ (d) $1-2 / n$
2. The kinetic energy, due to translational motion, of most of the molecules of an ideal gas at absolute temperature T , is:
(a) $kT ^3$ (b) $kT ^2$ (c) kT (d) $k / T$
3. The mean free path is the:
(a) length of the container that contains the gas
(b) mean of the square of the average distance between two successive collisions
(c) the average distance covered by a molecule between two successive collisions
(d) height of the container that contains the gas
4.The law of equipartition of energy is applicable to the system whose constituents are:
(a) in non random motion
(b) in random motion
(c) in orderly motion
(d) in rest
OR
Thermochemical calorie is equal to
(a) 41.48 joule (b) 4.148 joule (c) 4148 joule (d) 414.8 joule

Answer

1. (c) $1+2 / n$
Explanation: $1+2 / n$
2. (c) kT
Explanation: kT
3. (c) the average distance covered by a molecule between two successive collisions
Explanation: the average distance covered by a molecule between two successive collisions
4. (b) in random motion
Explanation: in random motion
OR
(b) 4.148 joule
Explanation: 4.148 joule

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Question 24 Marks

Clockwork refers to the inner workings of mechanical clock or watch (where it is known as "movement") and different types of toys which work using a series of gears driven by a spring. Clockwork device is completely mechanical and its essential parts are:
- A key (or crown) which you wind to add energy
- A spiral spring in which the energy is stored
- A set of gears through which the spring's energy is released. The gears control how quickly (or slowly) a clockwork machine can do things. Such as in mechanical clock/watch the mechanism is the set of hands that sweep around the dial to tell the time. In a clockwork car toy, the gears drive the wheels.
Winding the clockwork with the key means tightening a sturdy metal spring, called the mainspring. It is the process of storing potential energy. Clockwork springs are usually twists of thick steel, so tightening them (forcing the spring to occupy a much smaller space) is actually quite hard work. With each turn of the key, fingers do work and potential energy is stored in the spring. The amount of energy stored depends on the size and tension of the spring. Harder a spring is to turn and longer it is wound, the more energy it stores.

While the spring uncoils, the potential energy is converted into kinetic energy through gears, cams, cranks and shafts which allow wheels to move faster or slower. In an ancient clock, gears transform the speed of a rotating shaft so that it drives the second hand at one speed, the minute hand at $\frac{1}{60}$ of that speed, and the hour hand at $\frac{1}{3600}$ of that speed. Clockwork toy cars often use gears to make themselves race along at surprising speed.

1. What is the meaning of movement of old age mechanical clocks?
(a) The pendulum of the clock
(b) The gears which move the hands of the clock
(c) A spring and combination of gears which move the hands of the clock
(d) The hands of the clock
2. What type of energy is stored in the spring while winding it?
(a) Potential (b) Heat (c) Both kinetic and potential (d) Kinetic
3. When the spring of a clockwork uncoils
(a) Kinetic energy is converted into potential energy
(b) Potential energy is converted into kinetic
(c) Potential energy is converted into heat, light and sound energy
(d) Kinetic energy is converted into heat, light and sound energy
OR
More energy is stored in a spring if the
(a) Spring is larger, harder and wound fur a longer time
(b) Spring is smaller, harder and wound for a shorter time
(c) Spring is larger, harder and wound for a shurter time
(d) Spring is larger, softer and wound for a shorter time
4. In clockwork devices, ____________ transform the speed of a rotating ____________ to drive wheels slower or faster.
(a) Shaft, spring (b) shaft, gear (c) Gear, Shaft (d) Spring, gear

Answer

1. (c) A spring and combination of gears which move the hands of the clock
Explanation: Movement refers to the inner workings of mechanical clock using a series of gears driven by a spring.
2. (a) Potential
Explanation: Winding the spring means tightening a sturdy metal spring. It is the process of storing potential energy (forcing the spring to occupy a much smaller space) is actually quite hard work. With each turn of the key, fingers do work and potential energy is stored in the spring.
3. (b) Potential energy is converted into kinetic
Explanation: When the spring uncoils, the potential energy is converted into kinetic energy through gears, cams, cranks and shafts which allow wheels to move faster or slower.
OR
(a) Spring is larger, harder and wound fur a longer time
Explanation: With each turn of the key, fingers do work and potential energy is stored in the spring. The amount of energy stored depends on the size and tension of the spring. Harder a spring is to turn and longer it is wound, the more energy it stores.
4. (c) Gear, Shaft
Explanation: In an ancient clock, gears transform the speed of a rotating shaft so that it drives the second hand at one speed, the minute hand at $\frac{1}{60}$ of that speed, and the hour hand at $\frac{1}{3600}$ of that speed. Clockwork toy cars often use gears to make themselves race along at surprising speed.

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Physics Case study (4 Marks)

Case study (4 Marks)

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