. Here N A k=R called universal gas constant and its value is . J /mol. K.
So the ideal gas law can be written for μ mole of gas as PV = μ RT ( . ) This is called the equation of state for an ideal gas. It relates the pressure, volume and temperature of thermodynamic system at equilibrium. EXAMPLE .
A student comes to school by a bicycle whose tire is filled with air at a pressure kPa at °C. She travels km to reach the school and the temperature of the bicycle tire increases to °C. What is the change in pressure in the tire when the student reaches school? For this combined system, V becomes 2V, so C should also double to match with the ideal gas equation P V C ( ) .
It implies that C must depend on the number of particles in the gas and also should have the dimension of PV = JK . So we can write the constant C as k times the number of particles N. Here k is the Boltzmann constant ( . × − JK − ) and it is found to be a universal constant.
So the ideal gas law can be stated as follows PV = NkT ( . ) The equation ( . ) can also be expressed in terms of mole. Mole is the practical unit to express the amount of gas.
One mole of any substance is the amount of that substance which contains Avogadro number (N A ) of particles (such as atoms or molecules). The Avogadro’s number N A is defined as the number of carbon atoms contained in exactly g of C . Suppose if a gas contains μ mole of particles then the total number of particles can be written as Figure . Ideal gas law P,V,T,N P,V,T,N Two Separate systems P,2V,T,2N Single system - - - - Unit Heat and thermodynamics V = .
L P = kPa T = K Solution We