Home › Previous year questions › GATE 2024 AG › Question 61GATE 2024 AG – Question 61 Dairy and Food Engineering · Heat and Mass Transfer · 2 marks · Numerical answer
A steam-jacketed kettle holds250 kg liquid food with specific heat3.1 kJ/(kg·K). Steam is 121°C, heat-transfer coefficient2 kW/(m²·K),area .15 m². Using lumped capacity, find time to heat30→95°C in minutes, to two decimals.
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Show answer and explanation Correct answer: 52.00 to 56.00
Explanation For constant steam temperature,$mc_p\,dT/dt=hA(T_s-T)$. Integrating gives $t=mc_p/(hA)\ln[(T_s-T_i)/(T_s-T_f)]$. Thus $t=250(3.1)/[2(.15)]\ln(91/26)=3236.304$ seconds, because kJ/kW gives seconds. Divide by 60 to obtain **53.94 minutes**.
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