To raise the temperature of a certain mass of gas by 50° C at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100° C at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

Question

To raise the temperature of a certain mass of gas by 50° C at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100° C at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)? (A) 5 (B) 3 (C) 6 (D) 7

Tardigrade Admin · Accepted Answer

nC p (50)=160 nC v (100)=240 ⇒ ( C p /2 C v )=(160/240)=(&gamma;/2) ∴ &gamma;=(4/3) and f =(2/&gamma;-1)=6

5

3

6

7

nCp​(50)=160 nCv​(100)=240 ⇒2Cv​Cp​​=240160​=2γ​ ∴γ=34​ and f=γ−12​=6

$n C_{p} (50) = 160$
$n C_{v} (100) = 240$
$\Rightarrow \frac{C _{p}}{2 C _{v}} = \frac{160}{240} = \frac{γ}{2}$
$∴ γ = \frac{4}{3}$ and $f = \frac{2}{γ - 1} = 6$