JEE Main & Advanced Sample Paper JEE Main Sample Paper-47

  • question_answer
    One mole of an ideal monatomic gas is taken from temperature \[{{T}_{0}}\] to \[2{{T}_{0}}\] by the process\[p{{T}^{4}}=C\].Considering the following statements. Choose the correct alternative.
    I. Molar heat capacity of the gas is \[-\frac{3R}{2}\]
    II. Molar heat capacity of the gas is \[\frac{3R}{2}\]
    III. Work done is \[-3R{{T}_{0}}\]
    IV. Work done is 3 \[R{{T}_{0}}\]

    A)  Statements I and IV are correct           

    B)  Statements I and III are correct

    C)  Statements II and IV are correct          

    D)  Statements II and III are correct

    Correct Answer: B

    Solution :

     We have \[p{{T}^{-4}}=C,\,\,\,p{{V}^{4/3}}=C\] \[C=\frac{R}{\gamma -1}-\frac{R}{x-1}=\frac{3R}{2}-\frac{-3R}{2}\] \[\left( \text{Here},\,\,\gamma =\frac{5}{3}\,\,\text{and}\,x=\frac{4}{3} \right)\] Now, \[W=\frac{\eta R({{T}_{1}}-{{T}_{2}})}{\frac{4}{3}-1}=-3R{{T}_{0}}\]

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