When \(50 \mathrm{~g}\) of water at \(10^{\circ} \mathrm{C}\) is mixed with \(50 \mathrm{~g}\) of water at…

When \(50 \mathrm{~g}\) of water at \(10^{\circ} \mathrm{C}\) is mixed with \(50 \mathrm{~g}\) of water at \(100^{\circ} \mathrm{C}\). The resultant temperature is
  1. \(80^{\circ} \mathrm{C}\)
  2. \(55^{\circ} \mathrm{C}\)
  3. \(25^{\circ} \mathrm{C}\)
  4. \(45^{\circ} \mathrm{C}\)

Solution

If resulting temperature of the mixture is \(T^{\circ} \mathrm{C}\) then Heat gained by \(50 \mathrm{~g}\) water at \(10^{\circ} \mathrm{C}\), \(H_{\text {gain }}=m c \Delta T=50 c(T-10)\) Heat lost by \(50 \mathrm{~g}\) of water at \(100^{\circ} \mathrm{C}\) \(H_{\text {loss }}=m c \Delta T=50 c(100-T)\) According to principle of calorimetry, Heat gain \(=\) Heat loss \(\begin{array}{ll} \Rightarrow & H_{\text {gain }}=H_{\text {loss }} \\ \Rightarrow & 50 c(T-10)=50 c(100-T) \\ \Rightarrow & 2 T=110 \\ & T=55^{\circ} \mathrm{C} \end{array}\)

Asked in: AP EAMCET 2020 (17 Sep Shift 1)

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