Help with solutions of some questions from CAPF 2014 (13.7.2014)

Ghuspaith_22

the confusion is b/w (a) and (d). explanation for (a):
omitting hardcore gas equations, when the piston pushes the gas, pressure on the gas increases.
pressure= force/area. as the area is constant inside the piston shaft, it is the force which will matter(increase).
force= mass*acceleration. clearly, mass of the gas is also constant, so we are left with only acceleration.
acceleration= (v-u)/t, where v= final velocity, u=initial velocity and t=time.
time "t" is also unchanged.
as the acceleration has increased, it means v-u has increased, which implies an increase in 'V'.
now Kinetic energy =0.5*m*v^2.
now just backtrack.

hummingbird

the confusion is b/w (a) and (d). explanation for (a):
omitting hardcore gas equations, when the piston pushes the gas, pressure on the gas increases.
pressure= force/area. as the area is constant inside the piston shaft, it is the force which will matter(increase).
force= mass*acceleration. clearly, mass of the gas is also constant, so we are left with only acceleration.
acceleration= (v-u)/t, where v= final velocity, u=initial velocity and t=time.
time "t" is also unchanged.
as the acceleration has increased, it means v-u has increased, which implies an increase in 'V'.
now Kinetic energy =0.5*m*v^2.
now just backtrack.

thanks bro nice explanation.

Neanderthal

The kinetic energy of the gas will NOT change until and unless the Temperature changes. The Universal Gas Equation is PV=kT where P: Pressure, V:Volume, T: Temperature and k: proportionality constant.

Here, the process is assumed to be isothermal as conservation of energy is to be applied. So, if compression takes place, V decreases. Since P is inversely proportional to V, P increases and this causes a change of state.

Newton's Laws of Motion cannot be applied here because;
a. Gas particles are not macroscale bodies.
b. The gas is confined, not in free motion.

Therefore, the answer should ideally be B.

Neanderthal

@hummingbird

The text of the Act:
243Q. Constitution of Municipalities.-(1) There shall be constituted
in every State,-

(a) a Nagar Panchayat (by whatever name called) for a transitional
area, that is to say, an area in transition from a rural area to an
urban area;

(b) a Municipal Council for a smaller urban area; and

(c) a Municipal Corporation for a larger urban area,

Ergo, city councils is acceptable.

brkms

Re question (1): the process of compression by the piston in a gasoline engine is said to be an adiabatic or isentropic compression process. Id est, there is no heat transfer from or to the surroundings, and the entropy of the gas remains constant. The temperature of the gas *always* increases in such a process, while the entropy remains qualitatively constant. The T-s plot for such process is thus always a vertical line.

In simple terms - when compression occurs, the pressure exerted by the piston is utilized by the gas to raise its temperature, while its volume obviously decreases.

From the principle of conservation of energy - dQ = dU + dW (where dQ = heat transferred, dU= change in internal energy, dW = work done)

Since dQ here is zero, the internal energy of the gas increases in proportion to the work done by the piston. This implies an increase in temperature, and a concomitant increase in the gas' kinetic energy.

This principle lies at the heart of the operation of an internal combustion engine.

As far as change of state is concerned -in thermodynamic terms, the gas does indeed undergo a 'change of state', from (P1,V1,T1) to (P2,V2,T2), but I'd imagine by 'state' here they meant state of matter.

Because it's a non-engineering exam, I would presume the answer they were looking for is a simple 'pressure >, KE >' type relation.

absrockks

@Neanderthal
Since I have mechanical as my optional I think I can help you out here!
The question is rather vague with little clarity in options ....
As far as option A is concerned if examiner would have mentioned 'molecular kinetic energy' , it would have been a perfect pick.
Coming to option B, he has not clearly stated what he is implying by 'change in state' .... it can be change in terms of solid, liquid and gas..... or it can be a change in terms of gas parameters such as P,V,T .... as a student of GS it is natural to go with former implication (S,L,G), also its something obvious about latter being the examiner's intent since volume is definitely going to change in a compression process, isn't it?
As far as your explanation to option B is considered, you have a conceptual error while going in detail of a compression process of an automobile. Automobile engine operates either on a otto cycle or diesel cycle, both of these cycles have 'isoentropic compression' and not isothermal compression to conserve the energy and as a matter of fact temperature does change to a very large extent after compression process (25 C-> 600 C)

About option C chemical state change only after combustion process.

Therefore to this vague nature of question, I would have gone with option A.

Hope I'm clear.

absrockks

#totalagreement @brkms

Neanderthal

I am just going by the first part of the statement- 'according to the priciple of conservation of energy'. How is energy conserved in option A?

absrockks

conservation of energy itself is a vague proposition here! ... conservation of energy only applies to isolated systems .... while in the process of compression we are actually transferring energy to the gas by compressing it (how can you compress a gas without providing some energy to it?) ... so by conservation of energy examiner is only implying the adiabatic nature of process (no heat transfer) which leads to isoentropic process of compression....

brkms

I am just going by the first part of the statement- 'according to the priciple of conservation of energy'. How is energy conserved in option A?

Because the principle -as @absrockks mentioned- when applied to a thermodynamic process boils down to dQ = dU + dW. In other words, net work done plus net change in internal energy must equal net heat transfer.

Point to note here is they have specifically mentioned a gasoline engine. In petrol engines that work on the Otto cycle, there is NO transfer of heat during the compression process, which implies dQ = 0. Thus, the work done by the piston is absorbed by the gas to increase its temperature.