# Heat capacity problem-wher am i going wrong?

• debwaldy
In summary, the conversation discusses a question about finding the equilibrium temperature of a system after adding a certain amount of silver and an unknown substance. The method for solving the first part of the question is correct, resulting in an equilibrium temperature of 28 degrees celsius. However, there is trouble with the second part in finding the specific heat capacity of the unknown substance. After discussing and using the correct temperature change for the unknown substance, the final answer is 908.9 Jkg^-1 K^-1, which is close enough for the person asking for help.
debwaldy

## Homework Statement

Hi,so iv tried the following question and think my general methodology is correct but the final answer i am getting is wrong.ne ideas?

## Homework Equations

Question:a styrofoam cup contains 200g of water at 20 degrees celsius.What will be the equilibrium temp of the system after 100g of silver,initially at 300 degrees,has been added?you may assume that the heat capacity of the cup is negligible and that no heat is lost to the surroundings.

(b)a further 100g of an unknown substance,also at 300 degrees is now added to the system and the temperature rises by a further 26 degrees celsius
what is the specific heat capacity of the unknown substance?(the specific heat of water is 4180 Jkg^-1 K^-1 and that of silver 240 J kg^-1 K^-1)

## The Attempt at a Solution

so i got part a to work out correctly by saying:
heat energy lost by silver = heat energy gained by water
mass(silver).c(silver).(initial temp-final temp) =mass(water).c(water).(final temp-initial temp)

i.e. 0.1(240)(300-final temp)=0.2(4180)(final temp-20)
and found the equilibrium temp=28 degrees celsius,which i know is correct

its part b I am having trouble with:the correct answer is supposed to be 910 J kg^-1 K-1 but i keep getting 8600,by using the following,is it correct:

heat energy lost by unknown substance= heat energy gained by water and heat energy gained by silver

then:
mass(unknown).C(unknown).(26)=mass(water).c(water).(26) + mass(silver).c(silver).(26)

i.e. 0.1(c)(26) = 0.2(4180)(26)+0.1(240)(26)

=> c= 8600..which is wrong according to book?
any help wud be much appreciated
thanks

What is the temperature change for the unknown mass?[What is the final temperature for all three? = 28 + 26]

Using this, and your method, I get 908.9, which is close enough for me.

Last edited:
ok you that seems to make a lot more sense alright
thanks for the help

## 1. What is the definition of heat capacity?

Heat capacity is the amount of heat energy required to raise the temperature of a substance by one degree Celsius.

## 2. How is heat capacity calculated?

Heat capacity is calculated by dividing the amount of heat energy by the change in temperature of a substance.

## 3. What are the units of heat capacity?

The units of heat capacity are usually Joules per degree Celsius (J/°C) or Calories per degree Celsius (cal/°C).

## 4. Why is heat capacity important?

Heat capacity is important because it helps us understand how much heat energy is needed to change the temperature of a substance and how well a substance can store or release heat energy.

## 5. What are some factors that can affect heat capacity?

The factors that can affect heat capacity include the type of substance, its mass, and its temperature. The state of the substance (solid, liquid, gas) and any phase changes can also affect heat capacity.

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