Question

Column II gives certain systems undergoing a process. Column I suggests changes in some of the parameters related to the system. Mateh the statements in Column I to the appropriate processies) from Column II. Colum (A) The energy of the system is increased (B) Mechanical energy is provided to the system, which is converted into energy of random motion of its parts (C) Internal energy of the system is converted into its mechanical energy (D) Mass of the system is decreased Column II (p) System: A capacitor, initially uncharged Process: It is connected to a battery (q) System: \(A\) gas in an adiabatie container fitted with an adiabatic piston Process: The gas is compressed by pushing the piston (r) System: \(\mathbf{A}\) gas in a rigid container Process: The gas gets cooled due to colder atmosphere surrounding it (s) System: A heavy nucleus, initially at rest Process: The nucleus fissions into two fragments of nearly equal masses and some neutrons are emitted (t) System: A resistive wire loop Process: The loop is placed in a time varying magnetic field perpendicular to its plane

Short answer

(A) matches with (p), (B) matches with (q) and (t), (C) does not match with (r), and (D) matches with (s).

Step-by-step solution

Matching Process (p)

To match statement (A) with the processes, consider which system is increasing in energy. When a capacitor is connected to a battery (process p), the capacitor gets charged, increasing its electrical potential energy. Therefore (A) matches (p).

Matching Process (q)

For statement (B), mechanical energy being converted into random motion denotes an increase in random kinetic energy, which is thermal energy. When a gas is compressed adiabatically (process q) by pushing the piston, work is done on the system, and the internal energy increases, which increases the thermal motion of the gas molecules. Hence, (B) corresponds to (q).

Matching Process (r)

Statement (C) refers to the conversion of internal energy into mechanical energy. However, for a gas in a rigid container that is cooled (process r), the internal energy decreases, which does not match (C). This excludes (r) from matching (C).

Matching Process (s)

Process (s) involves a heavy nucleus fissioning into smaller parts, which involves a mass decrease due to the mass defect and the conversion of this mass into energy per Einstein's mass-energy equivalence. This means (D) matches (s). There's no mechanical energy conversion here, so (s) doesn't match (B) or (C).

Matching Process (t)

Finally, when a resistive wire loop is placed in a time-varying magnetic field (process t), it experiences induced current due to Faraday's law of electromagnetic induction. The mechanical energy of the moving magnetic field is converted to electrical energy, which due to the resistance of the loop, manifests as thermal energy as well. Therefore, (B) can also match (t).

Systematic Matching

Systematically matching the statements with processes:- (A) with (p), because energy of the system increases when the capacitor is charged.- (B) primarily with (q), because mechanical energy is provided to compress a gas which increases random motion (thermal energy). There is also a secondary match of (B) with (t) as mechanical energy of the magnetic field is converted into electrical and then to thermal energy.- (C) doesn't have a direct match but can be inferred to not be (r), as there's no conversion of internal to mechanical energy in the cooling of a gas.- (D) matches with (s) where the mass of a heavy nucleus is decreased during fission.

Key concepts

Energy Conversion

When we talk about energy conversion, we refer to the process of changing one form of energy into another. This concept is a cornerstone in the field of thermodynamics and plays an integral role in a multitude of physical systems and technological applications.

Take for instance the situation where mechanical energy is provided to a system; this energy is often transformed into another energy form, such as electrical or thermal energy, supporting the concept of conservation of energy. This is exactly what happens in both process (q) and process (t) in our exercise. In process (q), mechanical work done on a gas increases its internal energy, manifested as increased thermal motion. In process (t), the mechanical energy of a changing magnetic field is transferred to a wire loop, inducing electrical energy, which is then dissipated as thermal energy due to resistance within the loop.

Adiabatic Process

An adiabatic process is a thermodynamic process where no heat transfer takes place between a system and its environment. This means that all work done on or by the system goes into changing the system's internal energy instead of exchanging heat.

Within the context of our exercise, process (q) exemplifies an adiabatic process. When gas is compressed in an adiabatic container using an adiabatic piston, it's done so without the gas exchanging heat with its surroundings. The work of pushing the piston increases the gas's internal energy, which raises its temperature. Thus, any increase in random motion of the gas particles, and consequently any increase in temperature, is due purely to the work done on the system.

Nuclear Fission

The concept of nuclear fission involves a heavy nucleus, such as uranium or plutonium, splitting into smaller nuclei upon absorbing a neutron, releasing a vast amount of energy, additional neutrons, and reducing mass. The famous equation by Einstein, E=mc², explains that energy and mass are interconvertible; during fission, a tiny fraction of mass is converted into energy.

In the prescribed exercise, process (s) involves a heavy nucleus that undergoes fission, corresponding to statement (D). The exercise demonstrates the mass decrease in the system, which is attributable to the mass defect during fission—the principle behind the operation of nuclear reactors and atomic bombs. The energy released during this process is a result of the conversion of mass into energy.

Electromagnetic Induction

Lastly, electromagnetic induction is a phenomenon where an electric current is induced in a conductor due to a changing magnetic field. This principle is articulated by Faraday's Law, which essentially states that an electromotive force (EMF) is generated in a conductor when it experiences a variation in magnetic flux.

In our exercise's process (t), a loop of wire is exposed to a time-varying magnetic field, resulting in the induction of EMF within the loop. The electrical energy produced by this process may eventually be dissipated as heat due to the resistance of the wire, further exemplifying the conversion of mechanical energy into electrical and then thermal energy. Devices such as generators and transformers operate on the principle of electromagnetic induction, highlighting its significance in electrical engineering and technology.