કાર્નોટ ફ્રીજર \(0\,^oC\) તાપમાનવાળા પાણીમાંથી ઉષ્મા મેળવે છે અને \(27\,^oC\) તાપમાનવાળા રૂમમાં ઉષ્મા મુક્ત કરે છે.બરફની ગલનગુપ્ત ઉષ્મા \(336 \times 10^3\, J\,kg^{-1}\) છે. આ ફ્રીજર દ્વારા \(0\,^oC\) તાપમાનવાળા \(5\, kg\) પાણીનું બરફમાં રૂપાંતર કરવા માટે કેટલી ઉર્જાની જરૂર પડશે?

A \(1.51 \times {10^5}\,J\)
B \(1.68 \times {10^6}\,J\)
C \(1.71 \times {10^7}\,J\)
D \(1.67 \times {10^5}\,J\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(1.67 \times {10^5}\,J\)

Step-by-step Solution

Detailed explanation

\(\Delta H = mL = 5 \times 336 \times {10^3} = {Q_{sink}}\) \(\frac{{{Q_{sink}}}}{{{Q_{source}}}} - \frac{{{T_{sink}}}}{{{T_{source}}}}\) \(\therefore {Q_{source}} = \frac{{{T_{source}}}}{{{T_{sink}}}} \times {Q_{sink}}\) Energy consumed by freezer…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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