JEE MAIN - Physics (2021 - 25th July Morning Shift - No. 8)
A monoatomic ideal gas, initially at temperature T1 is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T2 by releasing the piston suddenly. If l1 and l2 are the lengths of the gas column, before and after the expansion respectively, then the value of $${{{T_1}} \over {{T_2}}}$$ will be :
$${\left( {{{{l_1}} \over {{l_2}}}} \right)^{{2 \over 3}}}$$
$${\left( {{{{l_2}} \over {{l_1}}}} \right)^{{2 \over 3}}}$$
$${{{l_2}} \over {{l_1}}}$$
$${{{l_1}} \over {{l_2}}}$$
Explanation
PVr = const.
TVr $$-$$ 1 = const.
$$T{(l)^{{5 \over 3} - 1}}$$ = const.
$${{{T_1}} \over {{T_2}}} = {\left( {{{{l_2}} \over {{l_1}}}} \right)^{{2 \over 3}}}$$
TVr $$-$$ 1 = const.
$$T{(l)^{{5 \over 3} - 1}}$$ = const.
$${{{T_1}} \over {{T_2}}} = {\left( {{{{l_2}} \over {{l_1}}}} \right)^{{2 \over 3}}}$$
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