A gas sample undergoes a reversible isothermal expansion. The figure gives the change ΔS in entropy of the gas versus the final volume Vf of the gas. The scale of the vertical axis is set by ΔSs = 68.4 J/K. How many moles are in the sample?
To determine the number of moles in the gas sample, we need to use the equation:
ΔS = nR ln(Vf/Vi)
where ΔS is the change in entropy, n is the number of moles, R is the ideal gas constant, Vi is the initial volume, and Vf is the final volume.
In the given problem, we have the value of ΔS (68.4 J/K) and the final volume Vf. Therefore, we need to find the initial volume Vi, which can be obtained from the graph.
By observing the graph, locate the point where ΔS is zero. This corresponds to the initial state of the gas sample.
Once you have identified the initial state point, note the corresponding volume Vi.
Now, we can solve the equation:
ΔS = nR ln(Vf/Vi)
Plugging in the given values for ΔS (68.4 J/K), the final volume Vf, and the initial volume Vi, and assuming R is the ideal gas constant, we can solve for n.
Therefore, the number of moles in the gas sample can be calculated using this equation.
To determine the number of moles in the gas sample, we need to use the ideal gas law, which states:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant
T is the temperature of the gas
The ideal gas law can be rearranged to solve for the number of moles:
n = PV / RT
In this case, the gas sample undergoes a reversible isothermal expansion, which means that the temperature remains constant. Therefore, we can simplify the equation to:
n = PV / RT
Since we do not have information about the pressure or temperature of the gas, we need to find an alternative way to determine the number of moles.
From the given information, we know that the change in entropy of the gas (ΔS) depends on the final volume (Vf). We can express this relationship as:
ΔS = nRln(Vf / Vi)
Where:
ΔS is the change in entropy
n is the number of moles
R is the ideal gas constant
ln is the natural logarithm
Vf is the final volume of the gas
Vi is the initial volume of the gas
In this case, the change in entropy (ΔS) is given as 68.4 J/K, and we are given a graph that shows the relationship between ΔS and Vf. By looking at the graph, we can find the corresponding value of Vf at ΔSs = 68.4 J/K.
Therefore, the next step is to find the value of Vf at ΔS = 68.4 J/K on the graph.