A 32.5-g iron rod, initially at 22.7 °C, is submerged into an unknown mass of water at 63.2 °C, in an insulated container. The final temperature of the mixture upon reaching thermal equilibrium is 59.5 °C. What is the mass of the water?

Video transcript

Hello everyone. Today, we have the following problem. A 55.5 g copper block initially at 20.9 °C is submerged in an unknown mass of water at 78.2 °C in an isolated container, insulated container. The final temperature of the mixture upon reaching thermal equilibrium is 45.5 °C. What is the mass of the water? So we're calling that when two substances of different temperatures are combined, the heat flows from the substance with higher heat to the substance with lower heat. And if they are combined in an isolated system, we say that the heat of our system is equal to the negative heat of our surroundings. And this just denotes that energy is being transferred in the form of heat. So we can then use this equation to surmise that the heat of our copper is equal to the heat. The negative heat of our water. Furthermore, to find the heat of our copper block, we can use the equation that the mass of our copper can be multiplied by the specific heat of our copper multiplied by the change in temperature expanding on this our mass is 55.5 g. Our specific heat can be found in the reference text is 0.3 85 joules per grams multiplied by Celsius. Let me multiply by the temperature difference. We see that the final temperature is 45.5 °C. And we subtract that from 20.9 °C. And when we do that, we get a, we get a heat for our cover block of 5 25.65 joules. So now we can determine the mass of our water. So using our equation from our first step, we can say that he he of our water is equal to its mass multiplied by its specific heat multiplied by the change in temperature. So since we said that our heat for hour copper is 5 25.65 joules, the water can have the opposite value. So we have our 525 0.65 joules. And then you go down to negative the mass, which we don't have multiplying that by its water specific heat, which can be found in reference to Texas as 4.18 joules per grams times degrees Celsius. And then we multiply by the diff change in temperature, which is that 45.5 °C. But this time, the water is 78.2 °C. Solving the map, we have 525.65 joules is equal to our negative mass multiplied by 136 or negative 1 36.6 86. And then when we solve for our initial mass, by dividing both sides by negative 1 36.6 86 we should arrive at a mass that equals 3.85 g or answer choice B and with that, we have solved the problem overall, I hope is helped. And until next time.