JEE MAIN - Physics (2020 - 9th January Evening Slot - No. 5)
Starting at temperature 300 K, one mole of an
ideal diatomic gas ($$\gamma $$ = 1.4) is first compressed
adiabatically from volume V1 to V2 = $${{{V_1}} \over {16}}$$. It is
then allowed to expand isobarically to volume 2V2. If all the processes are the quasi-static then
the final temperature of the gas (in oK) is (to the nearest integer) _____.
ideal diatomic gas ($$\gamma $$ = 1.4) is first compressed
adiabatically from volume V1 to V2 = $${{{V_1}} \over {16}}$$. It is
then allowed to expand isobarically to volume 2V2. If all the processes are the quasi-static then
the final temperature of the gas (in oK) is (to the nearest integer) _____.
Answer
1818TO1819
Explanation
T1V1$$\gamma $$–1 = T2V2
$$\gamma $$–1
$$300 \times {V^{{7 \over 5} - 1}} = {T_2}{\left( {{V \over {16}}} \right)^{{7 \over 5} - 1}}$$
$$ \Rightarrow $$ T2 = 300 × (16)0.4
Isobaric process
V = $${{nRT} \over P}$$
V2 = kT2... (1)
2V 2 = KTf... (2)
Tf = 2T2 = 300 × 2 × (16)0.4 = 1818 K
$$300 \times {V^{{7 \over 5} - 1}} = {T_2}{\left( {{V \over {16}}} \right)^{{7 \over 5} - 1}}$$
$$ \Rightarrow $$ T2 = 300 × (16)0.4
Isobaric process
V = $${{nRT} \over P}$$
V2 = kT2... (1)
2V 2 = KTf... (2)
Tf = 2T2 = 300 × 2 × (16)0.4 = 1818 K
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