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QPage 458: Q18: HC Verma: Concepts of Physics - Volume 2 The Special Theory of Relativity Page 458: Q18 Solution: Find the increase in mass when 1 kg of water is heated from 0�C …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often overlook that adding thermal energy to a system increases its relativistic mass, so the mass change $\Delta m$ must be calculated as a positive value using $\Delta m = Q/c^2$ rather than subtracting it from the rest mass.

Find the increase in mass when 1 kg of water is heated from 0�C to 100�C. Specific heat capacity of water = 4200 J kg−1 K−14200 \text{ J kg}^{-1} \text{ K}^{-1}.

Step-by-Step Verified Solution

**Answer:** Increase in mass = 4.67×10−124.67 \times 10^{-12} kg. **Step-by-Step Explanation:** Heat energy: Q=mcΔT=1×4200×100=4.2×105Q = mc\Delta T = 1 \times 4200 \times 100 = 4.2 \times 10^5 J. Mass equivalent: Δm=Q/c2=4.2×105/(9×1016)=4.67×10−12\Delta m = Q/c^2 = 4.2 \times 10^5/(9 \times 10^{16}) = 4.67 \times 10^{-12} kg.

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