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 sam 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) ?

Options

A. 5
B. 6
C. 3
D. 7

Answer

B

Explanation

At constant pressure,
`DeltaQ=nC_pDelta T implies 160=nC_p.50` ….(i)
At constant volume,
`DeltaQ=nC_V Delta T implies 240 - nC_V.100` ….(ii)
On dividing equation (i) by (ii)
`(160)/(240)=(C_P)/(C_V).(50)/(100) implies (C_P)/(C_V) = 4/3 =1+2/f`
`f=6`