Heat and Thermodynamics

Step 1: Write the adiabatic equation
An adiabatic process for an ideal gas can be written as:
pVγ=constant
Step 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+c
Here, 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=‌

∆log‌p

∆log‌V

From the graph, pick two points and subtract their values:
=‌

2.20−2.48

1.4−1.2

=‌

−0.28

0.2

=−1.4
Step 5: Interpret the value of γ
The slope m=−γ=−1.4, so:
γ=1.4
Step 6: Final answer
The ratio of the specific heat capacities of the gas is 1.4 .