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Heat and Thermodynamics question

2022 · Q152
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Heat and Thermodynamics question

2022 · Q152

NEETPhysicsHeat and ThermodynamicsMCQ+4 / −1

An ideal gas follows a process described by the equation PV2=CP{V^2} = CPV2=C from the initial (P1, V1, T1)({P_1},\,{V_1},\,{T_1})(P1​,V1​,T1​) to final (P2, V2, T2)({P_2},\,{V_2},\,{T_2})(P2​,V2​,T2​) thermodynamic states, where C is a constant. Then

  1. A
    If P1>P2{P_1} > {P_2}P1​>P2​ then V1>V2{V_1} > {V_2}V1​>V2​
  2. B
    If P1>P2{P_1} > {P_2}P1​>P2​ then T1<T2{T_1} < {T_2}T1​<T2​
  3. C
    If V2>V1{V_2} > {V_1}V2​>V1​ then T2>T1{T_2} > {T_1}T2​>T1​
  4. D
    If V2>V1{V_2} > {V_1}V2​>V1​ then T2<T1{T_2} < {T_1}T2​<T1​
View written solutionFree

Correct answer: D

We know,

$PV = nRT$

Given, $P{V^2} = $ constant

$\Rightarrow$ If $${P_1} > {P_2} \Rightarrow {V_1} < {V_2}$$

$$P{\left( {{{nRT} \over P}} \right)^2} = $$ constant

${P^{ - 1}}{T^2} = $ constant

$$ \Rightarrow P \propto {T^2}$$

i.e., if $${P_1} > {P_2} \Rightarrow {T_1} > {T_2}$$

Also, $$\left( {{{nRT} \over V}} \right){V^2} = $$ constant

$TV = $ constant

$\Rightarrow$ If ${V_2} > {V_1}$ then ${T_2} < {T_1}$

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