# A query about heat capacity and specific heat capacity

• ellieee
In summary, heat capacity is the amount of heat required to raise the temperature of an object by 1 Kelvin, measured in Joules per Kelvin (J/K). Specific heat capacity is the amount of heat required to raise the temperature of 1 kilogram of a substance by 1 Kelvin, measured in Joules per kilogram Kelvin (J/kgK) or Joules per kilogram Celsius (J/kg °C). The difference in units is due to the fact that heat capacity is a property of an object, while specific heat capacity is a property of a substance.
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

-

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

ellieee said:
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
Steve4Physics said:
@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?

ellieee said:
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?

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.

Steve4Physics said:

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

ellieee said:
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.

## 1. What is the difference between heat capacity and specific heat capacity?

Heat capacity is the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius, while specific heat capacity is the amount of heat energy required to raise the temperature of 1 gram of a substance by 1 degree Celsius.

## 2. How are heat capacity and specific heat capacity related?

Specific heat capacity is a characteristic property of a substance, while heat capacity depends on the mass and specific heat capacity of the substance. Heat capacity can be calculated by multiplying the mass of the substance by its specific heat capacity.

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

The units of heat capacity are joules per degree Celsius (J/°C) or calories per degree Celsius (cal/°C). The units of specific heat capacity are joules per gram degree Celsius (J/g°C) or calories per gram degree Celsius (cal/g°C).

## 4. How do different substances have different heat capacities and specific heat capacities?

Heat capacity and specific heat capacity depend on the physical and chemical properties of a substance, such as its mass, molecular structure, and phase (solid, liquid, or gas). Substances with higher molecular weights or stronger intermolecular forces tend to have higher heat capacities and specific heat capacities.

## 5. How can heat capacity and specific heat capacity be measured?

Heat capacity and specific heat capacity can be measured experimentally by using a calorimeter to measure the change in temperature of a substance when a known amount of heat is added or removed. These values can also be calculated using the known physical and chemical properties of a substance.

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