topic: thermochemistry
i'm not really sure how to go about his question. i'm not sure with formula to use. (perhaps Cspht= q/(m x deltaT)?)can you please help me step by step or give me a hint and i'll post my answer, pretty please?
"250g of hot coffee at 95 degree celsius are placed in a 0.200 kg mug at 20 degree celsius. The specific heat of the coffee is 4.00 Jg^-1K^-1 while that of the mug is 0.80 Jg^-1K^-1. Assuming that no heat is lost to the surroundings, what is the final temperature of the mug+coffee system?"
The sum of the heats gained is zero.
Heat gained by mug+heat gained by coffee=0
massmug*Cmug*(Tf-20)+masscoffee*Cwater*(Tf-95)=0
solve for Tf
oh! i get it now. q mug + q coffee = 0
after typing many numbers on my calculator i got the final temperature to equal 84.65 degrees C. I'm sure this is right, thank you very much :)
Sure! Let's start by breaking down the steps to solve this problem.
Step 1: Identify the information given in the question.
In this case, we have:
- Mass of the coffee (m1) = 250g
- Initial temperature of the coffee (T1) = 95°C
- Mass of the mug (m2) = 0.200kg
- Initial temperature of the mug (T2) = 20°C
- Specific heat capacity of the coffee (C1) = 4.00 Jg^-1K^-1
- Specific heat capacity of the mug (C2) = 0.80 Jg^-1K^-1
Step 2: Determine the heat transferred.
Since no heat is lost to the surroundings, the heat gained by the mug should be equal to the heat lost by the coffee. The equation for heat transfer is q = m x C x ΔT, where q is the heat transferred, m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.
The heat gained by the mug can be calculated as:
q2 = m2 x C2 x ΔT2
ΔT2 is the final temperature of the mug+coffee system minus the initial temperature of the mug.
The heat lost by the coffee can be calculated as:
q1 = m1 x C1 x ΔT1
ΔT1 is the initial temperature of the coffee minus the final temperature of the mug+coffee system.
Since q1 = -q2 (due to the conservation of energy), we can use this equation to solve for the final temperature of the mug+coffee system.
Step 3: Substitute the values and solve for the unknown variable.
Using the equations above, we can set the two heat equations equal to each other:
m1 x C1 x ΔT1 = -m2 x C2 x ΔT2
Since we are looking for the final temperature of the mug+coffee system, the equation can be rearranged as follows:
ΔT2 = (m1 x C1 x ΔT1) / (m2 x C2)
Now, you can substitute the given values into the equation to find ΔT2. Once you have ΔT2, you can calculate the final temperature by subtracting it from the initial temperature of the mug.