Determination of Cp of a gas
Regnault’s apparatus is used to measure Cp of a gas.
It has an arrangement to send gas through a pipe where in two manometers measure the pressure at two point and in between there is an adjusting screw to change the rate of flow. As the gas is flowing through this arrangement, adjusting screw is changed to maintain a constant difference of pressure between two manometers and this ensures that gas is at constant pressure when it is flowing through the calorimeter. This gas flows through an oil bath tank wherein it is given heat and then flows through the calorimeter wherein it gives out heat.
W = the water equivalent of the calorimeter with the coil
M = mass of water in the calorimeter
θ1 = temperature of the oil bath which gives heat to the gas.
θ2 = initial temperature of water in calorimeter
θ3 = Final temperature of water in calorimeter
n = amount of the gas (in moles) passed through the water
s = specific heat capacity of water
Cp of a gas. = (W + m) s (θ3 - θ2)/[n (θ1 – (θ2+ θ3)/2]
Determination of n = amount of the gas (in moles) passed through the water
It depends on the levels of mercury in the manometer attached to gas tank. If the difference in levels of the manometer is h and the atmospheric pressure (separately measured) is equal to a height H of mercury. The difference h is noted at the start of the experiment and at the end of the experiment. The pressure of the gas varies between p1 = H+h at the beginning to p2 = H+h at the end. Under the assumption of ideal gas
p1V = n1RT and p2V = n2RT
n is equal to n1 – n2 = (p1 - p2)V/RT
Determination of Cv of a gas
Joly’s differential steam calorimeter is used to measure Cv of a gas. The arrangement has two hollow copper spheres attached to two pans of a sensitive balance. In one of the spheres the gas for which Cv is to be measured is filled. At the start the temperature of the steam chamber without any steam is noted. It is the temperature of the gas at the beginning (θ1). Steam is sent through the steam chamber in which these two hollow spheres are there. Steam condenses on the hollow spheres and it collected in the pans attached to the hollow spheres. More steam condenses on the sphere having gas in it. After steady state conditions are reached temperature measurement is taken. This the final temperature of the gas.
m1 = the mass of gas taken or filled in the hollow sphere
m2 = the mass of extra steam condensed on the pan of the sphere having gas
θ1 = the temperature of the gas at the beginning
θ2 = the temperature of the gas at the end
L = Specific latent heat of vaporization of water.
M = molecular weight of the gas
Cv = Mm2L/[m1(θ1 – θ2)]