Verified Solution • 2025–26 Session moderate

QJEEM20Ph2327: JEE Main 2020 Physics - Class 11 JEEM20Ph2327 Solution: To raise the temperature of a certain mass of gas by 50 o C at…

To raise the temperature of a certain mass of gas by 50oC at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100oC 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)?

Multiple Choice Options

  • A 6
  • B 7
  • C 5
  • D 3

Step-by-Step Verified Solution

160=nCp50160 = n{C_p}50 ....(i)

240=nCv100240 = n{C_v}100 ....(ii)

Dividing (i) by (ii), we get

160240=CpCv×12{{160} \over {240}} = {{{C_p}} \over {{C_v}}} \times {1 \over 2}

⇒\Rightarrow CpCv{{{C_p}} \over {{C_v}}} = 43{4 \over 3}

We know,

γ=CpCv=1+2f=43\gamma = {{{C_p}} \over {{C_v}}} = 1 + {2 \over f} = {4 \over 3}

⇒f=6\Rightarrow f = 6

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