## Combined Gas Equation

It studies the variation of the volume of a given mass of a gas with both temperature and pressure.

If P_{1}, V_{1}, and T_{1} are the pressure, volume and temperature in the initial state respectively and P_{2}, V_{2} and T_{2} are the pressure, volume and temperature in the final state respectively, then

This equation is known as combined equation. Using this equation we can determine the state of the gas in any unknown condition if the initial state is known.

Now from equation (iii), we can write

PV=kT

The value of k depends on the amount of gas taken, for 1 gm of a gas the value of k depends upon the nature of gas and varies from one to another

For 1 mole of gas the value of k is constant called universal gas constant (R).

i.e. PV = RT

For n mole of gas the equation becomes

PV = nRT

This equation is called ideal gas equation.

**Significance of Universal Gas Constant:**

Therefore, Universal Gas Constant represents the work or energy required per mole of gas to increase its temperature by 1K.

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