×

# Ideal Gas Law And Absolute Zero

Top
FAQ
View Notes

The ideal gas law relates pressure P, volume V and temperature T of an ideal gas are by equation PV = nkBT, where n is the number of molecules of the gas, and kB is Bolztmann's constant. We can also write this as PV = NRT, where N denotes the number of moles of gas, and R is the gas constant. The ideal gas law is obeyed fairly well provided the density of the gas is not too high and these gases that obey it are called ideal gas. If the density is too high, the gas may condense to form a liquid, and the law fails in this case.

### Ideal Gas Law

The constant volume gas thermometer is made of a bulb that is  filled with a known fixed amount of a dilute gas attached to a mercury manometer. Now the bulb is brought in close contact with the source. The manometer attached to the bulb allows it to measure the exact pressure. The manometer contains a halfway filled mercury column and it is connected with a flexible tube to another partially filled column of mercury which is called the reservoir. Now the height of the mercury column is measured at the known temperature. Throughout this temperature measurement this height is fixed while the mercury in the reservoir is moved up or down.

This explains the gas thermometer. Now let us see how it works? This is where the ideal gas law comes in existence. The fundamental measurements of gas are done with pressure, P, volume, V and temperature, T. Also the SI Units of temperature is Kelvin; and T = t + 273.15 where t is in oC. The term pressure, volume and temperature of a gas are all interrelated and this interrelation was first explored by Robert Boyle. Boyle’s law states that when the temperature of a  gas is kept constant, PV = Constant.

This explains the gas thermometer. Now let us see how it works? This is where the ideal gas law comes in existence. The fundamental measurements of gas are done with pressure, P, volume, V and temperature, T. Also the SI Units of temperature is Kelvin; and T = t + 273.15 where t is in oC. The term pressure, volume and temperature of a gas are all interrelated and this interrelation was first explored by Robert Boyle. Boyle’s law states that when the sample gas temperature held constant, PV = Constant.

PV=Constant

French scientist Jacques Charles now came up with his law later named as Charles law. He discovered when the pressure of a gas is kept constant, the volume is related to the temperature by following equations

V/T = Constant.

These laws were later combined to yield one universal gas law known as the ideal gas law.

PV/T=constant

And the constant proportionality factor in this equation is the Universal Gas Constant, R ie, constant = nR.

where, n gives the number of moles of the gas in the sample

### Absolute Zero Temperature

Absolute zero is the defined temperature at which a thermodynamics system has the lowest energy. It corresponds to −273.15°C on Celsius scale and to −459.67°F on the Fahrenheit scale. The notion that there is an ultimately lowest temperature was suggested by the behaviour of gases at a very low pressure. It was observed that gases seem to contract indefinitely as the temperature decreases. Also an  ideal gas at constant pressure would reach zero volume at what is now called the absolute zero of temperature. Real gas in actual condenses to liquid or solid at some temperature higher than absolute zero that is why the ideal gas is only an assumption to real gas behavior.

### Significance of Absolute Zero

On extrapolating this graph, what we see is that between Pressure and temperature is shown below for different gases.

Now irrespective of the nature of gas we see that, the graphs always intercept the x axis at a point we call the absolute zero. This point represents the beginning of the Kelvin scale i.e Zero K. In the Celsius scale, it corresponds to -273.5 oC. This is possibly the coldest temperature. As a molecule gets colder, it’s energy, movements and vibrations decrease in amplitude. As we keep cooling it, at a point the atom will reach a state of minimum internal energy where the atom has lost all its energy.Thus we cay that absolute zero is a  state at which the enthalpy and entropy reach their minimum value and it the lowest limit on temperature scale.

Q1. What actually happens to the molecules of an ideal gas at Absolute Zero?

Ans. Theoretically the volume of an ideal gas molecule at absolute zero gas would be zero thus all the molecular motion would cease. But in actual, all gases condense to solids or liquids well above this point. At such low temperatures, gases assume non-traditional states, the Bose-Einstein and fermionic condensates.

Q2. Why can't the temperature go below the Absolute Zero?

Ans. On the absolute zero temperature scale, which is also called the Kelvin scale, it is not possible to go below zero – at least not in the sense of achieving colder than zero kelvin. Thus, nothing can be actually colder than absolute zero on the Kelvin scale.

Q3. How do you find the triple point of Water?

Ans. The temperature and pressure at which a substance can exist in equilibrium in the liquid, solid, and gaseous states only the term triple point is used, which refers to both the temperature and the pressure at which the three phases coexist in equilibrium. The triple point of water at  611.73 Pa is 273.16 K at. This is the basis of the Kelvin scale and it is equal to 0.01 оC, which is the freezing point of water.

Q4. Can a real gas actually reach Absolute Zero?

Ans. It appeared that an “ideal gas” at constant pressure would reach zero volume at what is now called the absolute zero of temperature but any real gases actually condenses to a solid or liquid state at some temperature higher than absolute zero. Thus  an ideal gas law is only an approximation to real gas behavior.