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The initial temperature of the mixture was +20^circ C The mixture froze at -1.5^circ C A total of 165 kJ of internal energy was transferred from the mixture to cool and freeze it. specific heat capacity of the mixture=3500J/kg^circ C specific latent heat of fusion of the mixture=255000J/kg Calculate the mass of the mixture. Give your answer to 2 significant figures. [6 mark

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The initial temperature of the mixture was +20^circ C The mixture froze at -1.5^circ C A total of 165 kJ of internal energy was transferred from the mixture to cool and freeze it. specific heat capacity of the mixture=3500J/kg^circ C specific latent heat of fusion of the mixture=255000J/kg Calculate the mass of the mixture. Give your answer to 2 significant figures. [6 mark

The initial temperature of the mixture was +20^circ C The mixture froze at -1.5^circ C A total of 165 kJ of internal energy was transferred from the mixture to cool and freeze it. specific heat capacity of the mixture=3500J/kg^circ C specific latent heat of fusion of the mixture=255000J/kg Calculate the mass of the mixture. Give your answer to 2 significant figures. [6 mark

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EvieMaster · Tutor for 5 years

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The mass of the mixture is approximately 0.65 kg.

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## Step 1: <br />First, we need to calculate the energy used to cool the mixture from \(+20^{\circ}C\) to \(0^{\circ}C\). This can be calculated using the formula:<br /><br />### \(Q = mc\Delta T\)<br /><br />where \(Q\) is the heat energy, \(m\) is the mass, \(c\) is the specific heat capacity, and \(\Delta T\) is the change in temperature.<br /><br />## Step 2:<br />Substitute the given values into the formula:<br /><br />### \(Q = m \times 3500 \times (20 - 0)\)<br /><br />## Step 3:<br />Rearrange the equation to solve for \(m\):<br /><br />### \(m = \frac{Q}{3500 \times 20}\)<br /><br />## Step 4:<br />The total energy transferred is 165 kJ, which is equal to \(165000 J\). The energy used to cool the mixture to \(0^{\circ}C\) is subtracted from the total energy to find the energy used to freeze the mixture.<br /><br />### \(Q_{\text{freeze}} = 165000 - Q\)<br /><br />## Step 5:<br />The mass of the mixture can then be calculated using the formula:<br /><br />### \(m = \frac{Q_{\text{freeze}}}{L_f}\)<br /><br />where \(L_f\) is the specific latent heat of fusion.<br /><br />## Step 6:<br />Substitute the given values into the formula:<br /><br />### \(m = \frac{165000 - Q}{255000}\)<br /><br />## Step 7:<br />Solve the equation to find the mass of the mixture.
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