The specific heat of water $=4200\mathrm{J}{\mathrm{k}\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$ ${}^{}{}^{}$ and the latent heat of ice $=3.4\times {10}^5\mathrm{J}{\mathrm{k}\mathrm{g}}^{-1}$ ${}^{}{}^{}$ . 100 grams of ice at $0^{?}\mathrm{C}$ ${}^{}$ is placed in $200\mathrm{g}$ $$ of water at ${25}^{?}\mathrm{C}$ ${}^{}$ . The amount of ice that will melt as the temperature of water reaches $0^{?}\mathrm{C}$ ${}^{}$ is close to (in grams):

<p><span contenteditable="false"> <math> <mrow></mrow> <mi>m</mi> <mo> (</mo> <mi>L</mi> <mo>)</mo> <mo>=</mo> <msub> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <msub> <mrow> <mrow> <mi>S</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mo> (</mo> <mi mathvariant="normal">Δ</mi> <mi>T</mi> <mo>)</mo> </math> </span></p><p><span contenteditable="false"> <math> <mo>⇒</mo> <mi mathvariant="normal">m</mi> <mfenced separators="|"> <mrow> <mrow> <mn>3.4</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfenced> <mo>=</mo> <mo> (</mo> <mn>200</mn> <mo>)</mo> <mo> (</mo> <mn>4200</mn> <mo>)</mo> <mo> (</mo> <mn>25</mn> <mo>)</mo> </math> </span></p><p><span contenteditable="false"> <math> <mo>⇒</mo> <mi mathvariant="normal">m</mi> <mo>=</mo> <mn>61.7</mn> </math> </span></p>

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