Easy Outside The Exam Hall, Nightmare Inside it

Have a look at this question asked in IIT JEE 2005

One calorie is defined as the heat required to raise the temperature of 1 g of water by 1°C in a certain
interval of temperature and at a certain pressure. The temperature interval and pressure is:
(A) 13.5°C to 14.5°C & 76 mm of Hg
(B) 6.5°C to 7.5°C & 76 mm of Hg
(C) 14.5°C to 15.5°C & 760 mm of Hg
(D) 98.5°C to 99.5°C & 760 mm of Hg

Most of the students taking the exam were clueless. I know all of you will shout- “very easy.” It is
because teachers started asking student to memorize this after 2005. It is an altogether different
matter that the question may not have any relevance for next 40 years of JEE.
Not very frequently, but JEE asks such deep probing theoretical questions. They are nightmare inside
the exam hall and easy outside.
Let me ask you one such question –
“What is the difference between thermal equilibrium and thermodynamics equilibrium?
Are they same?

Thermal Equilibrium

Place a block of wood and a block of metal in contact in a cold room maintained at a constant
temperature. After a long time, go and touch them. Do they feel equally warm? No. Due to
difference in their thermal conductivities the metal block feels much colder though both of them are
at the same temperature. Our sense of temperature is unreliable!
Then how do we even know that the two bodies are at same temperature? When two bodies are
placed in contact, their measurable properties like volume, resistivity etc. may initially change. But
after some time, we find that the changes have ceased. There are no further observable changes in
the measurable properties. This state is defined at thermal equilibrium and the two bodies are said
to have same temperature.
Now, consider an isolated system. We may observe that temperature is different for different parts
of the system. After a sufficiently long time the temperature will become same at all points and the
system is said to be in thermal equilibrium. If you switch on a heater in an insulated room for some
time, the air around the heater is much warmer than the air at a distant point. Even the walls close
to the heater will be warmer than a farther wall. A long time after the heater is switched off, every
point in the room acquires the same temperature. The room is in thermal equilibrium.

Mechanical Equilibrium

An isolated thermodynamic system may have variations in pressure at different locations. Parts of the system may move, expand or contract. Eventually, these movements stop and the system gains mechanical equilibrium. When the system is in mechanical equilibrium, the pressure may not be same everywhere! Hydrostatic pressure is not same at all points inside a tank full of water that is in equilibrium.

Chemical Equilibrium

An isolated system may have substance which react chemically. When all such reactions cease, we
say that the system is in chemical equilibrium.

Thermodynamic Equilibrium

A system which is in thermal, mechanical and chemical equilibrium is said to be in thermodynamic
equilibrium. Thermal equilibrium alone will not bring a system in thermodynamic equilibrium. While
the temperature is same at all points, the internal mechanical forces might be pulling/pushing the
parts and moving them. Only when such movements stops and there is no ongoing reaction, the
system attains thermodynamic equilibrium.

You are urged to think of a situation where a system is in thermal equilibrium but not in mechanical
equilibrium.

JEE rewards precision and accuracy. Casual learning of definition and formulae never helps.
Definition of calorie and thermodynamic equilibrium are just two examples.

SHASHI BHUSHAN TIWARI