Step 1: Write the adiabatic equation
An adiabatic process for an ideal gas can be written as:
pVγ=constantStep 2: Take logarithms on both sides
If we take the logarithm of both sides, we get:
log(p)+γlog(V)= constant This can be rearranged as:
log(p)=−γlog(V)+ constant Step 3: Compare to the standard line equation
This equation looks like the equation of a straight line:
y=mx+cHere,
y=log(p),x=log(V), and the slope
m=−γ.
Step 4: Find the slope from the graph
The slope of the line is:
m=From the graph, pick two points and subtract their values:
===−1.4Step 5: Interpret the value of
γThe slope
m=−γ=−1.4, so:
γ=1.4Step 6: Final answer
The ratio of the specific heat capacities of the gas is 1.4 .
