# A query about heat capacity and specific heat capacity

• ellieee

#### ellieee

Homework Statement:: why does heat capacity depend on the mass/size of the object when it's units is J/K , and why is specific heat capacity dependent on the material/substance when it's unit is J/kgK?
Relevant Equations:: Q=Cθ
Q=mcθ

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## Answers and Replies

a) It takes 10 times more heat to heat 10 liters of water by 1 degree than it takes to heat 1 liter of water by 1 degree. Heat capacity is the amount of heat it takes to heat an object per temperature increase.

b) Different materials have different internal structure and therefore require more or less energy to raise their temperatures by a given amount. Specific heat capacity is therefore a material property that depends on the material.

sophiecentaur
per temperature increase.
but the temperature of the object didn't increase though? it's the mass right?

but the temperature of the object didn't increase though? it's the mass right?
No. The mass of each object remains the same. It is just that something of the same material that has twice the mass will take twice the energy to raise the temperature.

@ellieee, try working through these questions, paying attention to units at all stages. Post your answers if you still have a problem.

A metal ‘X’ has a specific heat capacity of c=1000J/(kg·K).

(Note, a change of 1K is the same as a change of 1ºC, so the unit can also be written J/(kg.ºC).

Q1. How much energy is needed to raise the temperature of 1kg of X by:
a) 1K?
b) 5K?

Q2. How much energy is needed to raise the temperature of 3kg of X by:
a) 1K?
b) 5K?

Q3. What is the heat capacity, C, of a 3kg of block of X?

Q4. Using your answer from Q3, how much energy is needed to raise the temperature of the block by:
a) 1K?
b) 5K?

Q5. Compare your answers to Q2 and Q4. Are they the same? Do you see why?

sophiecentaur
@ellieee, try working through these questions, paying attention to units at all stages. Post your answers if you still have a problem.

A metal ‘X’ has a specific heat capacity of c=1000J/(kg·K).

(Note, a change of 1K is the same as a change of 1ºC, so the unit can also be written J/(kg.ºC).

Q1. How much energy is needed to raise the temperature of 1kg of X by:
a) 1K?
b) 5K?

Q2. How much energy is needed to raise the temperature of 3kg of X by:
a) 1K?
b) 5K?

Q3. What is the heat capacity, C, of a 3kg of block of X?

Q4. Using your answer from Q3, how much energy is needed to raise the temperature of the block by:
a) 1K?
b) 5K?

Q5. Compare your answers to Q2 and Q4. Are they the same? Do you see why?
hmm I still don't get it.. Q2 was being derived through specific heat capacity, while Q4 was being derived through heat capacity, so what point can that prove?

hmm I still don't get it.. Q2 was being derived through specific heat capacity, while Q4 was being derived through heat capacity, so what point can that prove?
It wasn't meant to prove anything! It was meant to provide some insight to help you answer your original questions!

Here' a different approach. Can you answer these:

What is the definition of the heat capacity of an object?
From this definition, find the unit in which heat capacity is measured.

What is the definition of the specific heat capacity of a substance?
From this definition find the unit in which specific heat capacity is measured.

It wasn't meant to prove anything! It was meant to provide some insight to help you answer your original questions!

Here' a different approach. Can you answer these:

What is the definition of the heat capacity of an object?
From this definition, find the unit in which heat capacity is measured.

What is the definition of the specific heat capacity of a substance?
From this definition find the unit in which specific heat capacity is measured.
heat capacity : J/K
specific heat capacity: J/kgK or J/kg °C

heat capacity : J/K
specific heat capacity: J/kgK or J/kg °C
You haven't given the definitions (in words). From each definition, you can work out the unit. Then you'll understand why the unit is used.