https://ejercicios-fyq.com/ Ejercicios Resueltos, Situaciones de aprendizaje y VÍDEOS de Física y Química para Secundaria y Bachillerato es SPIP - www.spip.net https://ejercicios-fyq.com/local/cache-vignettes/L144xH25/siteon0-da713.png?1758361862 https://ejercicios-fyq.com/ 25 144 https://ejercicios-fyq.com/Calorimetry-final-temperature-of-a-mixture-8297 https://ejercicios-fyq.com/Calorimetry-final-temperature-of-a-mixture-8297 2024-09-02T03:37:09Z text/html es F_y_Q Calorimetry Temperature SOLVED <p>100 g of water at is mixed with 300 g of water at . What will be the final temperature of the mixture?</p> - <a href="https://ejercicios-fyq.com/Energy-and-heat" rel="directory">Energy and heat</a> / <a href="https://ejercicios-fyq.com/Calorimetry" rel="tag">Calorimetry</a>, <a href="https://ejercicios-fyq.com/Temperature" rel="tag">Temperature</a>, <a href="https://ejercicios-fyq.com/SOLVED" rel="tag">SOLVED</a> <div class='rss_texte'><p>100 g of water at <img src='https://ejercicios-fyq.com/local/cache-vignettes/L50xH17/513d73beaa9ae362e57006fb5c16c382-3f234.png?1733002651' style='vertical-align:middle;' width='50' height='17' alt="10\ ^oC" title="10\ ^oC" /> is mixed with 300 g of water at <img src='https://ejercicios-fyq.com/local/cache-vignettes/L55xH42/df740a9202d22e3b71445ce1efcd70b9-39cd9.png?1732977318' style='vertical-align:middle;' width='55' height='42' alt="40\ ^oC" title="40\ ^oC" />. What will be the final temperature of the mixture?</math></p></div> <hr /> <div <div class='rss_ps'><p>The heat lost by the hot water is equal to the heat gained by the cold water.<br/> <br/> For the hot water: <img src='https://ejercicios-fyq.com/local/cache-TeX/7677908c73c18f810c657a3f3848082a.png' style="vertical-align:middle;" width="337" height="23" alt="\color[RGB]{2,112,20}{\bm{Q_{hot} =m_{hot}\cdot c_e(H_2O)\cdot (T_f - T_i)}}" title="\color[RGB]{2,112,20}{\bm{Q_{hot} =m_{hot}\cdot c_e(H_2O)\cdot (T_f - T_i)}}" /> <br/> <br/> For the cold water: <img src='https://ejercicios-fyq.com/local/cache-TeX/911e7b6c22a10519790749321e41f11e.png' style="vertical-align:middle;" width="349" height="23" alt="\color[RGB]{2,112,20}{\bm{Q_{cold} =m_{cold}\cdot c_e(H_2O)\cdot (T_f - T_i)}}" title="\color[RGB]{2,112,20}{\bm{Q_{cold} =m_{cold}\cdot c_e(H_2O)\cdot (T_f - T_i)}}" /> <br/> <br/> The heat lost is considered negative, and the heat gained is positive: <br/> <br/> <img src='https://ejercicios-fyq.com/local/cache-TeX/473d251aa211eaf398290e1af004d3f5.png' style="vertical-align:middle;" width="144" height="21" alt="\color[RGB]{2,112,20}{\bm{Q_{cold}= - Q_{hot}}}" title="\color[RGB]{2,112,20}{\bm{Q_{cold}= - Q_{hot}}}" /> <br/> <br/> Equating the heat exchanges: <br/> <br/> <img src='https://ejercicios-fyq.com/local/cache-TeX/54be27a30b1898d68fd5755ec36078b6.png' style="vertical-align:middle;" width="588" height="23" alt="100\ g\cdot c_e(\ce{H2O})\cdot (T_f - 10\ ^oC) = - 300\ g\cdot c_e(\ce{H2O})\cdot (T_f - 40\ ^oC)" title="100\ g\cdot c_e(\ce{H2O})\cdot (T_f - 10\ ^oC) = - 300\ g\cdot c_e(\ce{H2O})\cdot (T_f - 40\ ^oC)" /> <br/> <br/> Eliminating the specific heat of water from the equation and simplifying: <br/> <br/> <img src='https://ejercicios-fyq.com/local/cache-TeX/caa7375d89ade215b0e3db49af3831be.png' style="vertical-align:middle;" width="275" height="23" alt="-T_f + 10\ ^oC = 3\ T_f - 120\ ^oC" title="-T_f + 10\ ^oC = 3\ T_f - 120\ ^oC" /> <br/> <br/> Solving for the final temperature: <br/> <br/> <p class="spip" style="text-align: center;"><img src='https://ejercicios-fyq.com/local/cache-TeX/2b227ae2c39d10cec30a6a5602010763.png' style="vertical-align:middle;" width="325" height="34" alt="130\ ^oC = 4\ T_f\ \to\ \fbox{\color[RGB]{192,0,0}{\bm{32.5\ ^oC = T_f}}}" title="130\ ^oC = 4\ T_f\ \to\ \fbox{\color[RGB]{192,0,0}{\bm{32.5\ ^oC = T_f}}}" /></p> </math></p></div>