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JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion Question Bank Critical Thinking

  • question_answer
    In an industrial process 10 kg of water per hour is to be heated from 20°C to 80°C. To do this steam at 150°C is passed from a boiler into a copper coil immersed in water. The steam condenses in the coil and is returned to the boiler as water at 90°C. how many kg of steam is required per hour. (Specific heat of steam = 1 calorie per gm°C, Latent heat of vaporisation = 540 cal/gm)

    A)            1 gm                                        

    B)            1 kg

    C)            10 gm                                      

    D)            10 kg

    Correct Answer: B

    Solution :

                       Suppose m kg steam required per hour Heat released by steam in following three steps (i) When 150°C steam \[\xrightarrow[{{Q}_{1}}]{}100{}^\circ C\] steam     Q1 = mcSteam Dq = m ´ 1 (150 ? 100) = 50 m cal (ii) When 150°C steam \[\xrightarrow[{{Q}_{2}}]{}100{}^\circ C\] water     Q2 = mLV = m ´ 540 = 540 m cal (iii) When 100°C water \[\xrightarrow[{{Q}_{2}}]{}90{}^\circ C\] water     Q3 = mcW Dq = m ´ 1 ´ (100 ? 90) = 10 m cal Hence total heat given by the steam Q = Q1 +Q2 + Q3 = 600 mcal        ... (i) Heat taken by 10 kg water \[Q'=m{{c}_{W}}\Delta \theta =10\times {{10}^{3}}\times 1\times (80-20)=600\times {{10}^{3}}cal\] Hence Q = Q¢ Þ 600 m = 600 ´ 103 Þ m = 103 gm = 1kg.


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