# Could you help me with this thermodynamics question?

#### Zeynaz

Problem Statement
A baby bottle contains 180mL milk. The heat capacity of the bottle and the milk is 770 J/K. The density of the milk is 1.04 kg/dm^3

a) calculate the heat capacity of the bottle
Relevant Equations
Q=C*dT
Q=cm*dT
Density =mass/Volume
So, I converted the V (milk) to m3 and found 1.8E-4 m3 and i already know the density so i found the mass of the milk in the bottle.

Mmilk= 1.9E-7 kg
Normally i would try to connect it with the formulas above but i dont know temperature. I am not sure how i can connect the dots.

Thanks!

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#### TSny

Homework Helper
Gold Member
Probably you can assume that the specific heat capacity for the milk is the same as for water.
How many Joules of heat must be added to the milk alone in order to raise the temperature of the milk by 1 Kelvin?

Also, check your calculation of the milk's mass.

EDIT: I don't think you should assume that the specific heat capacity of the milk is the same as for water. Were you given a value for milk, maybe in a table?

Last edited:

#### Zeynaz

Probably you can assume that the specific heat capacity for the milk is the same as for water.
How many Joules of heat must be added to the milk alone in order to raise the temperature of the milk by 1 Kelvin?

Also, check your calculation of the milk's mass.

EDIT: I don't think you should assume that the specific heat capacity of the milk is the same as for water. Were you given a value for milk, maybe in a table?
Yes you are right there is a table where i can find the density and specific heat capacity of all substances. So in this case the SHC of milk is 3.9E3.
And i think i found the right mass for the milk which is 0.187kg. The answer should be 40J/K but i dont know how to get there

#### Zeynaz

Yes you are right there is a table where i can find the density and specific heat capacity of all substances. So in this case the SHC of milk is 3.9E3.
And i think i found the right mass for the milk which is 0.187kg.
So i know the combines SHC of milk and the bottle. I know the SHC of the milk. Am i just supposed take it as an average and say: SHC bottle+milk= (SCHmilk +SHCbottle)/2 ?

#### TSny

Homework Helper
Gold Member
Am i just supposed take it as an average and say: SHC bottle+milk= (SCHmilk +SHCbottle)/2 ?
No, that won't work. Did you try to calculate the amount of heat required to increase the temperature of just the milk by 1 Kelvin?

How much heat would be required to increase the total milk-and-bottle system by 1 Kelvin?

#### Zeynaz

No, that won't work. Did you try to calculate the amount of heat required to increase the temperature of just the milk by 1 Kelvin?

How much heat would be required to increase the total milk-and-bottle system by 1 Kelvin?
For Q-milk= m,milk * c = 729.3 J
For Q Bottle-Milk= (m-milk+m-bottle)*770
But i dont know mass of the bottle.
Meanwhile, i also tried to find the mass of the bottle first by equating Q milk with Q bottle and i got 0.760kg and tried to work my way but it didnt really work.
Another way,
When i write: Qmilk-bottle = Q-bottle + Q milk and apply mass of the bottle, it doesnt give me the right answer and also i dont know Q b-m

#### TSny

Homework Helper
Gold Member
Q-milk= m,milk * c = 729.3 J
OK. This is the heat that must be added to the milk alone in order to increase its temperature by 1 K.
For Q Bottle-Milk= (m-milk+m-bottle)*770
But i dont know mass of the bottle.
Note that the value of 770 J/K is not the specific heat capacity, $c$, of the system. Rather, it is the heat capacity, $C$, of the system. It is important to distinguish these. Can you express in words the meaning of the quantity 770 J/K?

Meanwhile, i also tried to find the mass of the bottle first by equating Q milk with Q bottle and i got 0.760kg and tried to work my way but it didnt really work.
There is no reason to expect that Q for the milk will be the same as Q for the bottle.

#### Zeynaz

OK. This is the heat that must be added to the milk alone in order to increase its temperature by 1 K.
Note that the value of 770 J/K is not the specific heat capacity, $c$, of the system. Rather, it is the heat capacity, $C$, of the system. It is important to distinguish these. Can you express in words the meaning of the quantity 770 J/K?

There is no reason to expect that Q for the milk will be the same as Q for the bottle.
That to increase 1 Kelvin of bottle-milk system we need 770 joules so in that case, technically i can take 770 as Q for bottle-milk system right?

#### TSny

Homework Helper
Gold Member
Yes. You also know the heat required to raise the temperature of just the milk by 1 K. Can you deduce how much heat is required to raise the temperature of just the bottle by 1 K?

#### Zeynaz

Thank you for your help I figured it out!

#### TSny

Homework Helper
Gold Member
OK, good work.

"Could you help me with this thermodynamics question?"

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