JEE MAIN - Physics (2020 - 3rd September Evening Slot - No. 11)
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)?
6
7
5
3
Explanation
$$160 = n{C_p}50$$ ....(i)
$$240 = n{C_v}100$$ ....(ii)
Dividing (i) by (ii), we get
$${{160} \over {240}} = {{{C_p}} \over {{C_v}}} \times {1 \over 2}$$
$$ \Rightarrow $$ $${{{C_p}} \over {{C_v}}}$$ = $$ {4 \over 3}$$
We know,
$$ \gamma = {{{C_p}} \over {{C_v}}} = 1 + {2 \over f} = {4 \over 3}$$
$$ \Rightarrow f = 6$$
$$240 = n{C_v}100$$ ....(ii)
Dividing (i) by (ii), we get
$${{160} \over {240}} = {{{C_p}} \over {{C_v}}} \times {1 \over 2}$$
$$ \Rightarrow $$ $${{{C_p}} \over {{C_v}}}$$ = $$ {4 \over 3}$$
We know,
$$ \gamma = {{{C_p}} \over {{C_v}}} = 1 + {2 \over f} = {4 \over 3}$$
$$ \Rightarrow f = 6$$
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