I don't understand What is the calculation I need to do and how do I get the answer?

Question

Specific heat (C)is defined as the amount of heat (q) necessary to produce a temperature change (T) of 1°C per gram of substance. We can express this mathematically as: C = q m x ∆T (1) Where m equals the mass of the substance. We can rearrange this equation to solve for q: q = m x C x T (2) One technique we can use to measure the amount of heat involved in a chemical or physical process is known as calorimetry. Calorimetry is used to measure amounts of heat transferred to or from a substance.

In today’s experiment, we will mix liquids with two different starting temperatures. After they are mixed, both liquids will reach the same temperature after a sufficient amount of time. Because of the law of conservation of energy, the heat released by the hot liquid will be absorbed by the cold liquid, so we can say: q(hot liquid) = - q(cold liquid) (3) This sign change is necessary because of heat is lost, then q is negative. Conversely is heat is gained q is positive.In today’s experiment, you will calculate how much cold liquid (milk) must be added to a hot liquid (coffee) so that the final temperature of the mixture is 90 deg C. The coffee will be at 95 deg C and the milk will be at 4 deg C. Then you will use the Virtual Lab at chemcollective.org to verify your calculations. To perform the necessary calculations, substitute equation (2) into equation (3), and get the following (equation 4): m(coffee) x C(coffee) x T(coffee) = - m(milk) x C(milk) x T(milk) (4) For our calculations, assume that coffee and milk have the same heat capacity and the same density as water (4.184 J/g deg C) and 1.0g/mL, respectively. Now we have all the information we need to plug in values for m(coffee), C(coffee , T (coffee), C(milk), and T (milk), we can solve for the mass of milk (m(milk)), and then use the density of milk to convert the mass of milk to the volume of milk needed.

Answer 1

Hello, Veronica,

The specific heat of a substance is a measure for how much energy is required to heat or cool an amount of that substance for every 1 degree C. [Be aware that the units for specific heat often are given in alternative units of J/moleC or even J/ml*C. Also, Joules may be replaced with other energy equivalents, such as ergs, kwh, kJ, etc. Always be aware of the units].

The amount of heat to be taken from the coffee to cool it to 90C from 95C can be calculated, once we have a mass. No mass is given here, so I'll assume 100ml of coffee as an example. At a density of 1 g/ml, that is exactly 100g.

To calculate the amount of heat (in Joules) that needs to be removed, use the equation q = c*m*(T2-T1), where T1 and T2 are the initial and final temperatures, respectively.

In this example, we get J = 4.18J/gC*(100g)*(90C - 95C) = -2,090J, or -2.09 kJ.

The grams and C cancel, leaving Joules. The answer is negative since it is giving off energy. The energy has "been subtracted," so to speak.

We need to know how much milk at 4C must be added to absorb this much energy. Again, we can use the same equation, structured as follows:

2,090J = (4.18J/gC)*m*(90C - 4C)

I removed the minus sign on the Joules coming in, since the heat is being added (absorbed) by the cooler milk. Working through this calculation I get an answer of 5.81 g of 4C milk is needed to lower 100g of 95C coffee to 90C. At a density of 1g/ml, this is also 5.81ml.

Seems a little low to me, so please check the calculations. But, thinking about it, I assumed a rather meager amount of coffee to start.

I hope this helps,

Bob