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)?
Solution
$160 = n{C_p}50$ ....(i)<br><br>$240 = n{C_v}100$ ....(ii)<br><br>Dividing (i) by (ii), we get<br><br>${{160} \over {240}} = {{{C_p}} \over {{C_v}}} \times {1 \over 2}$
<br><br>$\Rightarrow$ ${{{C_p}} \over {{C_v}}}$ = ${4 \over 3}$
<br><br>We know,
<br><br>$\gamma = {{{C_p}} \over {{C_v}}} = 1 + {2 \over f} = {4 \over 3}$<br><br>$\Rightarrow f = 6$
About this question
Subject: Physics · Chapter: Thermodynamics · Topic: Zeroth and First Law
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