Zeroth law feels obvious, so what does it actually let us define? And are heat and work state variables?

7 answers & replies

• [+][–]Siddharth RaoDropperSample· 1mo ago

  What it gives us is the concept of temperature. If C is a thermometer and it shows the same reading when put in contact with A and with B, then the law guarantees that A and B would be in equilibrium with each other, with no net heat flow, without ever putting A and B together. That is what makes a thermometer a meaningful instrument: "temperature" becomes a property that has the same value for all systems in thermal equilibrium.

  It's "zeroth" because it was recognised as fundamental after the first and second laws were already named, and it logically comes before them.

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  • [+][–]Meera Patel11thSample· 1mo agoAuthor

    Thank you, "temperature as something with the same value in equilibrium" is exactly the idea I was missing. Writing the thermometer example in my answer.

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• [+][–]Tanvi Deshmukh12thSample· 1mo ago

  Table time!!

  Variable	Type	State variable?
  Pressure $P$	intensive	yes
  Temperature $T$	intensive	yes
  Volume $V$	extensive	yes
  Mass / number of moles	extensive	yes
  Internal energy $U$	extensive	yes
  Heat $Q$, Work $W$	n/a	no

  Extensive = depends on the size of the system (double the system, the value doubles). Intensive = doesn't depend on the size (cut the gas in half, P and T stay the same).

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• [+][–]Sara Fernandes11thSample· 1mo ago

  One more idea to include: thermal equilibrium means no net flow of heat between the systems, which happens when their temperatures are equal. NCERT also talks about walls: an adiabatic wall doesn't let heat pass, a diathermic wall does. So two gases separated by a diathermic wall will eventually come to the same temperature. In the 3-mark answer, mentioning this earns the "thermal equilibrium" mark.

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• [+][–]Arjun Nair12thSample· 1mo ago

  On heat and work, the classic trap is to think a body "contains" heat. A state variable depends only on the current state, not how it got there. Internal energy qualifies: the same $U$ for given $T$, $V$ for an ideal gas whichever path you took.

  Heat and work are energy in transit across the boundary of the system. They depend on the path. For example, taking a gas from state A to state B by a different route (constant pressure then constant volume, versus the other way round) gives different $W$ and $Q$, but the difference $Q - W$ is always the same: $\Delta U$. A body doesn't "contain" heat, it contains internal energy, and heat is the name for the energy that flows due to a temperature difference.

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  • [+][–]Sara Fernandes11thSample· 1mo ago

    ohh energy in transit, not stored. I used to say "heat content" all the time, thanks Arjun!

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• [+][–]Nisha Verma12thSample· 1mo ago

  Equation of state = a relation between state variables that fixes the behaviour of the system. For an ideal gas it is $PV = \mu RT$, where $\mu$ is the number of moles and $R = 8.31$ J mol⁻¹ K⁻¹. If you know any two of $P, V, T$ you know the third. Without it, we cannot plot P–V diagrams or calculate work in processes like isothermal expansion.

  For the 3-mark answer I'd write: zeroth law statement, one line on temperature, one line on thermal equilibrium (no heat flow, same temperature) and the example of the thermometer.

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