Interview question from Thermodynamics ( Part 1 )

Index

Q Why zeroth law is called zeroth law?
Q What is the efficiency of the Carnot cycle? 80% or 90% or 100% or what?
Q Can you explain the Adiabatic v/s Reversible Adiabatic Process?
Q There are so many reversible cycles like the Otto cycle, Diesel cycle, and Brayton cycle. Why Carnot is the most efficient of all?
Q What is the heat flow at zero temperature difference? 

Q. Why zeroth law is called zeroth law?

There are 4 laws in thermodynamics. It's one of them.

Zeroth is not the name of a scientist. 

1st law of thermodynamics- talks about the internal energy of the system... The energy you can store and another which cannot be stored(it enters the system and goes out).

2nd Law of thermodynamics- tells us whether any physical process is feasible or not.

Tells us about an important quantity called "Entropy". There's a law that says that the entropy of an isolated system can never decrease. So if there's heat interaction where the entropy is decreasing that process is not possible.

3rd law of thermodynamics- says absolute zero temperature is unattainable...

But why? Can we prove it? We invented the thermometer to calculate the temperature. But how does a thermometer measure temperature?

We know that if body A is in thermal equilibrium with body B and body B is in thermal equilibrium with body C. Does it mean A is also in thermal equilibrium with C. YES...

Thermal equilibrium means the same temperature.

We had 3 laws of thermodynamics.. Zeroth law came last. Chronologically the concept of this thermal equilibrium came at the last but as per the importance it was put at first.. and became zeroth law. Because 3rd law says 0K is unattainable but how do we measure it? So temperature is the basic thing it has to be at the first.. but before 1 comes 0.. so it is called Zeroth law..

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Q. What is the efficiency of the Carnot cycle? 80% or 90% or 100% or what?

Heat can only be subtracted or added from processes 1 to 2 and 3 to 4. 4 to 1 and 2 to 3 are isentropic processes. No interaction in isentropic processes. 

Isentropic processes <=> Reversible adiabatic process.

So heat can be added from 1 to 2 and rejected at 3 to 4. Once you solve this Carnot cycle you find that:

So What is the efficiency of the Carnot cycle? That depends on what's min. temperature and what's the max temperature?

But we say the Carnot cycle is the most efficient? What's the meaning of that?

Let's take a hypothetical situation, T(max) is 1000C and T(min) is 1C. If you calculate the efficiency it will be very high... It can be 99.999. But it cannot be 100%.

so if I calculate, I would get the range.

Here efficiency 0 means no work is produced. It is not an engine at all.

Efficiency cannot be 1 too. This means heat rejected is 0. 100% WORK. It's called a perpetual motion machine of 2nd type. But 100% is not possible. 2nd law of thermodynamics Kelvin Plank statement.

 So what's the efficiency? It can be more than 0 and less than 1.

Q. Can you explain the Adiabatic v/s Reversible Adiabatic Process?

Adiabatic- means heat flow is zero. No heat interaction between the system and its surrounding. And this is a real process.. Normally it is a fast process. The potential gradient will be more. Usually the more the temperature difference between bodies fast will be the flow of heat.

Reversible Adiabatic Process-  They are isentropic.(Otto cycle, Diesel cycle, Carnot cycle, Brayton cycle, all are isentropic)

Usually, reversible processes have -

Ideal situation. Very slow process. It is not a real process. So it's like an ideal gas concept. We assume it for simplifications. 

The equation we use PV powers gamma = constant . We use it for reversible adiabatic, not for adiabatic.

So if in the question it is mentioned that the process is very slow and adiabatic it is a reversible adiabatic process. If it is mentioned the process is adiabatic it is adiabatic means we can't use these above equations.

How to make process adiabatic. 5 ways-

1. Insulation

2. Isolation

3. Less space(throttling)

4. Less time available (Fast process) (Free expansion)

5. System + surrounding (Universe)

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Q. There are so many reversible cycles like the Otto cycle, Diesel cycle, and Brayton cycle. Why Carnot is the most efficient of all?

The thing is all the reversible cycles are internally reversible. This means their processes are reversible. But in the Carnot cycle, all the processes are internally reversible + externally reversible also. This means the thermodynamic system and surrounding, whatever interaction is taking place, it is taking place reversibly.

If you draw the PV diagram of the Otto cycle, you find that 1 to 2 is the compression process, and 2 to 3 is the heat addition process. Heat addition is the isochoric process(Constant volume). 4 to 1 is isochoric heat rejection. So heat addition and heat rejection are isochoric processes.

In the case of the Carnot cycle. Heat addition is an isothermal process(Constant temperature).

Carnot cycle is a cycle where all the heat is added at the maximum temperature and the entire heat is rejected at the minimum temperature. 

Concept of Available energy-  Available energy in the heat energy is the maximum work possible that you can extract from that heat. So if I give Heat energy Q1, how much energy is used from the Q1 to work is its available energy. And Available energy is more if heat is supplied at very high temperatures.

In the Carnot cycle entire heat we are supplying is at T(max) and in the Otto cycle heat is supplied at the mean temperature of  T at 2 and 3. Let's call it T(m1). and the Entire heat is rejected at mean temperature of T at 4 and 1. let us call it T(m2). So heat is not supplied at maximum temperature and not rejected at a minimum temperature in the Otto cycle. 

That means Q1 applied in the Carnot cycle is more than in the Otto cycle. It means the Carnot cycle will extract more heat and will do more work and reject less heat than the Otto cycle. It means heat is not properly utilized in the Otto cycle. But Carnot assumes that the entire heat is supplied at maximum temperature and the entire heat is rejected at minimum temperature. It means the Carnot cycle will utilize the entire available energy and rejects the minimum available energy.

Remember efficiency = Work(W)/Heat supplied(Q1)

Now, what it means to be externally reversible?

Tell me, Is it possible that Heat(Q1) can flow if the source temperature and temperature at which heat is supplied to the engine are the same? 

Remember to heat to flow we need to have a potential gradient, which means temperature difference. When the heat is supplied and the potential gradient is very less or the temperature difference is very less, that is called reversible heat transfer. 

So when heat is supplied and the temperature difference through which heat is supplied is very small that is called reversible heat flow. So Q1 is supplied reversibly and Q2 is rejected reversibly as well. It means, not all the processes inside the working system inside, is reversible but heat supplied from outside sources and heat rejected at the sink is also reversible.

So it means the Carnot cycle is reversible internally and externally as well. No other engine is externally also reversible.

So conclusively, The maximum available energy can be utilized in the Carnot engine because the entire heat is supplied at maximum temperature and heat at maximum temperature has maximum available energy or work-producing potential in it. And heat is rejected at minimum temperature, it means when it goes out with minimum available energy in it. Means its utilizing the entire available energy.

That's the reason the Carnot cycle is the most efficient cycle.

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Q. What is the heat flow at zero temperature difference?

The formula for heat flow is dQ = mcdT , 

                                      c= specific heat

                                    mc = heat capacity                

                                   dT= temperature change

What will happen during the Isothermal process? T=const and dT=0

(dQ)T = 0, but this is incorrect...

Let's understand...  There are 2 ways by which heat can flow,

Sensible heating and Latent heating

Sensible heating -  Temperature change. e.g If we supply heat or put a container of water above the burner, it will increase the temperature of the water. The phase remains the same.

Latent heating- T constant, Phase change takes place (Solid to liquid or liquid to gas and so on.)

E.g: If the temperature increases to 100C it will start boiling and converting to vapors.

Latent heat of sublimation, Latent heat of Ablimation, Latent heat of condensation, etc are phase change processes.

The heat flow formula will be different in both cases.

In Sensible heating                                                 In Latent heating

  dQ=mcdT                                                               Q= mL

Isothermal process -  T remains constant.. dT = 0

here we cannot use dQ= mcdT. If dT=0 isothermal then mc=dQ/dT=> infinity.

It means the body would have infinite heat capacity. And for infinite heat capacity, we cannot define c. For isochoric it's C(v), for isobaric it's C(p), but no C(t) for isothermal. So specific heat or heat capacity for the isothermal process is not defined because of its Latent heating or constant temperature heating process.

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