2. Questions Bank
  3. Railways
  4. NTPC (Technical Ability)
  5. Thermodynamics

Railways NTPC (Technical Ability) Thermodynamics Question Bank Thermodynamics

  • question_answer
    For a Carnot engine \[{{T}_{1}}>{{T}_{2}}.\] When \[{{T}_{2}}\] is decreased by \[\Delta T\] with \[{{T}_{1}}\] remaining same then efficiency is \[{{\eta }_{1}},\] and when \[{{T}_{1}}\] is increased by \[\Delta T\] with \[{{T}_{2}}\] remaining same, efficiency is \[{{\eta }_{2}}.\] Which one of the following is the correct expression for \[\left( {{\eta }_{1}}-{{\eta }_{2}} \right)?\]

    A) \[\frac{({{T}_{2}}-{{T}_{1}})\,\,\Delta \,T+{{(\Delta \,T)}^{2}}}{{{T}_{2}}({{T}_{2}}+\Delta \,T)}\]

    B) \[\frac{({{T}_{2}}-{{T}_{1}})\,\,\Delta \,T+{{(\Delta \,T)}^{2}}}{{{T}_{1}}({{T}_{1}}+\Delta \,T)}\]

    C) \[\frac{({{T}_{1}}-{{T}_{2}})\,\,\Delta \,T+{{(\Delta \,T)}^{2}}}{{{T}_{1}}({{T}_{1}}+\Delta \,T)}\]

    D) \[\frac{({{T}_{1}}-{{T}_{2}})\,\,\Delta \,T+{{(\Delta T)}^{2}}}{{{T}_{1}}({{T}_{1}}+\Delta T)}\]

    Correct Answer: C

    Solution :

    \[{{\eta }_{Carnot}}=1-\frac{{{T}_{2}}}{{{T}_{1}}}\] \[{{\eta }_{1}}=1-\frac{{{T}_{2}}-\Delta T}{{{T}_{1}}}\] \[{{\eta }_{2}}=1-\frac{{{T}_{2}}}{{{T}_{1}}+\Delta T}\] \[{{\eta }_{1}}-{{\eta }_{2}}=\frac{{{T}_{2}}}{{{T}_{1}}+\Delta T}-\frac{{{T}_{2}}+\Delta T}{{{T}_{1}}}\] \[=\,\,\frac{{{T}_{1}}{{T}_{2}}-({{T}_{1}}{{T}_{2}}+{{T}_{2}}.\Delta T-{{T}_{1}}.\Delta T-{{\left( \Delta T \right)}^{2}})}{{{T}_{1}}({{T}_{1}}+\Delta T)}\] \[=\,\,\frac{({{T}_{1}}-{{T}_{2}})\,\Delta T+{{(\Delta T)}^{2}}}{{{T}_{1}}({{T}_{1}}+\Delta T)}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner