Question

If work done by an ideal diatomic gas in a process from A to B as shown in PV graph is 20J. If increase in internal energy of the gas is x, (in joule) then

• A. x is a perfect square
• B. x has 9 factors
• C. x is a perfect number
• D. sum of factors of x is 215

Answer 1

Answer: (A), (B)

x is a perfect square
x has 9 factors

$W=Area=\frac{1}{2}PV=\frac{1}{2}nR\Delta T=20J$
Now the change in internal energy is given as
$\frac{f}{2}nR\Delta T$(here f is the number of degree of freedom)
For a diatomic gas f=5. Thus we get
$\Delta U=\frac{5}{2}nR\Delta T=100J.=x$
The number 100 is a perfect square and it has 9 factors including 1, 2, 4, 5, 10, 20, 25, 50 and 100.