Hey, I'm struggling a bit with this thermal energy question:

One major cost in the brewing history is the cost of energy used in running a plant. Much of the heating plant is accomplished by the cooling and or condensing of steam.

When 50.0 mg of griest is heated from 25.0 C to 43.1 C the temperature of 560 Mg of steam decreases from 120.0 C to 117.0.
Calculate the heat capacity of the griest.

I know how to manipulate the formula, but how do I go from this?
I know I would have to first find the thermal energy.. but which mass do I use? And would I have to convert Mg to grams?

Thank you (:

I have no idea what griest is? Can you help. Is it a liquid, solid, gas? What's the specific heat?

To calculate the heat capacity of the griest, you need to use the equation:

Q = mcΔT

Where Q is the thermal energy, m is the mass of the substance being heated (griest in this case), c is the specific heat capacity of the substance, and ΔT is the change in temperature.

In this question, you are given the change in temperature for both the griest and the steam. However, you are only given the mass of the griest, not the specific heat capacity (c).

To get the specific heat capacity of the griest, you need to rearrange the equation:

c = Q / (m * ΔT)

Now, you need to calculate the thermal energy (Q) separately for the griest and the steam.

For the griest:
Q(griest) = (m(griest)) * c(griest) * ΔT(griest)

For the steam:
Q(steam) = (m(steam)) * c(steam) * ΔT(steam)

Given:
m(griest) = 50.0 mg
ΔT(griest) = (43.1°C - 25.0°C)

m(steam) = 560 Mg (Megagrams, also known as metric tons)
ΔT(steam) = (117.0°C - 120.0°C)

Note: 1 Mg = 1 million grams

To find the thermal energy (Q) for both substances, you multiply the mass by the specific heat capacity and the change in temperature.

For the griest:
Q(griest) = (50.0 mg) * c(griest) * [(43.1°C - 25.0°C)]

For the steam:
Q(steam) = (560 Mg) * c(steam) * [(117.0°C - 120.0°C)]

Since the question asks for the heat capacity of the griest, you only need the thermal energy for the griest. However, it is important to note that the ΔT for both substances is connected because they are in thermal contact.

Once you have the thermal energy Q(griest), you can rearrange the equation for specific heat capacity to solve for c(griest):

c(griest) = Q(griest) / (m(griest) * ΔT(griest))

At this point, you have all the values required to calculate the heat capacity of the griest. You don't need to convert the mass of the steam from Mg to grams for this specific calculation.

I hope this explanation helps you understand how to approach this thermal energy question! Let me know if you have further questions.