Two substances, A and B, initially at different temperatures,
com...

Question

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?

Accepted Answer

Welcome back everyone in this example, we have to consider two substances M. And N. So we're told that substance M. Has a mass of 5.16 g and is initially at 18.6 degrees Celsius. On the other hand, we're told that substance end has a mass of 22.3 g and is initially at 56.4 degrees Celsius. We're told that the two substances come into contact with each other to reach a thermal equilibrium and that the final temperature of both substances is 49.7 degrees Celsius. So given the specific capacity of substance N. As 2.34 jewels divided by grams times degrees Celsius, we need to calculate the specific key capacity of substance M. So what we want to recall since we have our specific heat capacity mentioned as well as the term thermal equilibrium is our specific heat capacity formula. Where we recall that we can calculate heat or cue from taking our massive, our substance multiplied by its respective heat capacity, which is then multiplied by the difference in temperature delta T. And we want to recall that our heat Q. Is expressed in units of jewels. We want to recall that our mass is going to be expressed in units of gramps. And we want to recall that are specific specific heat capacity. C. As given in the prompt for substance N. Is expressed in units of jewels divided by grams times degrees Celsius. And then lastly we want to recall that for our difference in temperature, that's the final temperature minus the initial temperature. And it's given in degrees Celsius here. So what we should recognize is again, as the prompt states these two substances are at a thermal equilibrium and because we recognize that substance M is at the lower temperature of 18.6 degrees Celsius. Whereas Substance N is at a higher temperature of 56.4 degrees Celsius. We would say that the heat of substance M is equal to the negative heat of substance N. And that is due to the fact that Substance N. Or substance M absorbs some of substance ends heat or substance ends extra heat since it's at a higher temperature. Because we understand that our variable Q. Represents the flow of heat or the flow of energy. And so the extra heat present in our substance end at the higher temperature will flow to our lower temperature of substance M in order to reach this thermal equilibrium. And because we understand this relationship, we can go ahead and reinterpret our specific heat capacity formula to set that equal for both substances. So we would say that for substance M. Its mass times its specific heat capacity, multiplied by the difference in temperature it's final temperature minus its initial temperature, this is all for substance M is equal to the negative change of substance ends mass times its specific heat capacity and will actually use a different color for this side. So we'll use purple multiplied by the difference in temperature for substance N. Are equal to one another. So this is the relationship that we're going to use to find our specific heat capacity for substance M because it's going to be an unknown variable here. So we're going to plug in what we know into our formula. And above we are given the mass of substance em in the prompt as 5.16 g multiplied by the variable C. Which we need to solve for M. And then for the final minus initial temperature. Because the prompt states that these substances are at a thermal equilibrium. Both temperatures of both substances is 56.4°C as their final temp. So we plugged that in below 56.4°C. And in the prompt were given the initial temperature of substance M. And correction here. So this is actually the temperature of substance n. So it says that the equilibrium temperature is going to be 49.7°C. So these are the final temperatures for both of our substances. And this is what we will plug in actually 49.7°C. And the initial temperature of substance M. According to the prompt is a value of 18.6°C. So this completes our portion for substance M. And we're setting this equal to the right hand side of our equation for substance N. Which is a negative change multiplied by substance mass given in the prompt as 22.3 g. Multiplied by substance ends specifically capacity given in the prompt as 2. jewels divided by grams times degree Celsius. And just to make more room, we're going to scoot this over. So then we have to multiply by the difference in temperature. So as we stated, the thermal equilibrium final temperature for both substances is 49.7°C. Given in the prompt subtracted from the initial temperature of substance and given in the prompt as 56.4°C. So this is our full formula plugged in. And now we just want to simplify to sell for our variable c. So our first simplification will begin with the subtraction from our temperatures on both sides and on the left hand side we will be able to simplify to our mass 55.16 g. Sorry, that's the one there. This is multiplied by the variable c. for em. And then the difference in temperature we should get a result of 31.1°C for substance M moving on, we have our change for substance N where we have that mass still there in grams. Multiplied by the specific capacity. And sorry, let's use a different color here. So the difference in temperature for substance and is going to give us a result of negative 6.7°C. And so to continue our simplification we want to go ahead and take the product of the right hand side as well as our terms on the left hand side and what we would be able to get. And let's make sure we fill this in for substance and so what we would be able to get for our left hand side is the specific capacity variable multiplied by the product result of 160.476. And we have units of grams now being multiplied by degrees Celsius here. So this is going to be set equal to our right hand side. Where we will we will get a product equal to 349.6194. And as far as our units we will be able to cancel out grams in the numerator with grams in the denominator here as well as Celsius. And the numerator with Celsius in the denominator here, leaving us with units of jewels. So this is going to be in jewels. And so now to isolate for our specific capacity of substance. Mm We will divide both sides by our 160.476 g times degrees C. And so this will cancel out on the right hand side, isolating specific capacity C. And we would say that the specific capacity for substance M is equal to a final value of 2.18. And we have units of joules divided by grams times degrees Celsius. And these are our proper units for specifically capacity. So this will be actually our final answer to complete this example, as are specifically capacity of substance. So I hope that everything I reviewed was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

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