CBSE-XI-Physics
47: The Special Theory of Relativity
- #18Find 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-1.Ans : Given:
Mass of water, m = 1 kg
Specific heat capacity of water, s = 4200 J kg-1 K-1
Change in temperature, ∆θ = 100°C
Heat energy required, Q = ms∆θ
Q = 1 × 4200 × 100
= 420000 J
This energy is converted into mass. Thus,
`` \,\mathrm{\,Increase\,}\,\mathrm{\,in\,}\,\mathrm{\,mass\,}\,\mathrm{\,of\,}\,\mathrm{\,water\,}\,\mathrm{\,on\,}\,\mathrm{\,heating\,}=∆m=\frac{Q}{{c}^{2}}``
`` \Rightarrow ∆m=\frac{420000}{{\left(3\times {10}^{8}\right)}^{2}}``
`` =\frac{42}{9}\times \frac{{10}^{4}}{{10}^{16}}``
`` \Rightarrow ∆m=4.66\times {10}^{-12}\,\mathrm{\,kg\,}\approx 4.7\times {10}^{-12}\,\mathrm{\,kg\,}``
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