Question

3. If a gas has n degrees of freedom, ratio of specific heats of gas is:
a) 1+n
b)1+
c)1+
0)1 +
n
2​

Answer 1

The ratio of specific heat of gas is

D) 1+2/n is correct

1. The internal energy of a gas is given as
2. $E=N(\frac{1}{2}nKT)$
3. N is no molecules (Avogadro's number)
4. k is Boltzmann constant
5. T is the temperature of gas
6. Gas constant (R)= NK
7. So now internal energy can be written as
8. $E=\frac{1}{2}nRT$
9. Specific heat at constant volume is given as $C_{v}=(\frac{dE}{dT}) _{v}$
10. $C_{v} =\frac{n}{2}R$
11. $C_{p} =C_{v} +R=(\frac{n}{2} +1)R$
12. The ratio of specific heat of gas is
13. $\frac{C_{p} }{C_{v} } =\frac{(n+\frac{1}{2} )R}{\frac{n}{2} R}=1+\frac{2}{n}$