A silver block, initially at 58.5 °C, is submerged into 100.0 g of water at 24.8 °C, in an insulated container. The final temperature of the mixture upon reaching thermal equilibrium is 26.2 °C. What is the mass of the silver block?

Video transcript

Hello everyone. Today, we have the following problem. A silver block initially at 58.5 °C is submerged into 100 g of water at 24.8 °C in an insulated container. The final temperature of the mixture upon reaching thermal equilibrium is 26.2 °C. What is the mass of the silver block? So this is relating the heat equation and it is a heat transfer from something that is hot to something that is cold. And so we can say that the heat of the silver is negative since we are losing heat, it is losing heat. And then we can say it is equal through the heat of the water, which would be positive because it is gaining heat. Furthermore, we can expand this reaction such that we have negative, we have the mass can be multiplied by our specific heat capacity that is then multiplied by the change in temperature for silver. And then we do the same for our water except that it is positive. So we don't have the mass of our silver. So we have the mass of our silver that can be multiplied by the specific heat capacity of our silver, which is 0.235 joules divided by grams times Celsius multiplied by the change in temperature. And the change in temperature was that we went from the final temperature which is 26.2 °C, we subtracted from the initial temperature which is 58.5 °C. And then we equal that to the heat of the water. So we have 100 g of our water multiplied by its specific heat which is 4.184 joules. Do I buy grams times Celsius? They multiply that by the change in temperature which will be 26.2 three °C. And then we subtract that from the 24.8 °C. That was for the water. No, to work numbers around, we will solve for the mass of the silver, which will essentially end up being the 100 g multiply by 4.18 joules divided by grams times the degrees of Celsius multiply by 1.4 degrees Celsius divided by our specific heat for our silver, which is 0.235 joules divided by grams times C degrees Celsius. And it'll be multiply that specific capacity by negative 32.3 °C. And this would give us a final mass of 77.1 g or answer twice a as our answer overall, I hope this helped. And until next time