Two substances, A and B, initially at different temperatures, come into contact and reach thermal equilibrium. The mass of substance A is 6.15 g and its initial temperature is 20.5 °C. The mass of substance B is 25.2 g and its initial temperature is 52.7 °C. The final temperature of both substances at thermal equilibrium is 46.7 °C. If the specific heat capacity of substance B is 1.17 J/g•°C, what is the specific heat capacity of substance A?

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Welcome back everyone to another video. Two substances C and D initially at different temperatures come into contact and reach thermal equilibrium. The mass of substance C is 12.1 g and its initial temperature is 19.5 °C. The mass of substance D is 28.3 g and its initial temperature is 63.4 °C. The final temperature of both substances at thermal equilibrium is 41.5 °C. If the specific heat capacity of substance C is a 1.67 joules per gram per Celsius. What is the specific heat capacity of substance? D? There are four answer choices. A 0.363 B 2.76 C 1.39 and D 0.717 all given in joules per gram per Celsius. So now let's remember the law of energy conservation which tells us that if we have a heat exchange, then the heat of substance C plus the heat of substance D would be equal to zero because the energy is conserved. The energy or the amount of heat lost by one substance is equal to the amount of heat absorbed by the other. And let's also remember that heat is specific heat capacity multiplied by mass multiplied by the change in temperature T final minus T initial. So now if we start with substance C, we can say that mass of C multiplied by the specific heat capacity of C multiplied by the final temperature minus the initial temperature of substance C plus mass of D multiplied by the specific heat capacity of D multiplied by the final temperature minus the initial temperature of substance D. This should be equal to zero. And now we are solving for the specific heat capacity of substance D. So if we rearrange this equation, we can essentially state that CD which is the specific heat capacity of D would be equal to negative. Now, we are taking mass of sea specific heat capacity of C we multiply by the change in temperature. And that we divide that result by the mass of the multiplied by the, the final temperature minus the initial temperature of D. We have our expression, we can simply calculate the result. So let's substitute the givens starting with mass of C. We know that it's 12.1 g. We're multiplying that by the specific heat capacity of 1.67 Juul per gram per Celsius. Now we multiply by the final temperature, right, the final temperature is 41 0.5 °C. We subtract the initial temperature of sea. It states 19.5 °C. And now we have to divide all of that by the mass of D which is 28 0.3 g. And then we multiply by the final temperature minus the initial temperature of D, we know the initial temperature is 63.4 °C. And now if we calculate the result, we get zero point 717 Juul per gram per Celsius, which essentially corresponds to the answer choice D. That would be it for today. And thank you for watching.

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Key Concepts

Thermal Equilibrium

Specific Heat Capacity

Heat Transfer Equation