JEE MAIN - Physics (2020 - 7th January Morning Slot - No. 10)
A litre of dry air at STP expands adiabatically to a volume of 3 litres. If $$\gamma $$ = 1.40, the work done by air is : (31.4 = 4.6555) [Take air to be an ideal gas]
60.7 J
100.8 J
90.5 J
48 J
Explanation
$${P_1}V_1^\gamma = {P_2}V_2^\gamma $$
$$ \Rightarrow $$ P2 = P1$${\left[ {{{{V_1}} \over {{V_2}}}} \right]^\gamma }$$
= 105 $$ \times $$ $${\left[ {{1 \over 3}} \right]^{1.4}}$$
Work done = $${{{P_1}{V_1} - {P_2}{V_2}} \over {\gamma - 1}}$$
= $${{{{10}^5} \times {{10}^{ - 3}} - {{{{10}^5}} \over {{3^{1.4}}}} \times 3 \times {{10}^{ - 3}}} \over {1.4 - 1}}$$
= 88.7 J $$ \approx $$ 90.5 J
$$ \Rightarrow $$ P2 = P1$${\left[ {{{{V_1}} \over {{V_2}}}} \right]^\gamma }$$
= 105 $$ \times $$ $${\left[ {{1 \over 3}} \right]^{1.4}}$$
Work done = $${{{P_1}{V_1} - {P_2}{V_2}} \over {\gamma - 1}}$$
= $${{{{10}^5} \times {{10}^{ - 3}} - {{{{10}^5}} \over {{3^{1.4}}}} \times 3 \times {{10}^{ - 3}}} \over {1.4 - 1}}$$
= 88.7 J $$ \approx $$ 90.5 J
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