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Why gases have 2 specific heats?

Why gases have 2 specific heats?

Akhil Francis Specific heat capacity at constant pressure and specific heat capacity at constant volume……It is because heat energy supplied at constant Pressure changes both Internal Energy and also does Some amount of work…..while Heat energy supplied at constant volume only changes it’s internal energy and does not do any work as Volume is a constant…

A simple relation between two specific heat capacities are given by

Cp – Cv=R

Is this the answer?

Heat! Heat! Heat!

Thermal vibration of a segment of protein alph...
Thermal vibration of a segment of protein alpha helix. The amplitude of the vibrations increases with temperature. (Photo credit: Wikipedia)

A glass ball at -10 degrees C is placed in 500 ml of water at 20 degrees C. The final temp is 15 degrees C.
A. How much heat is lost by the water
B. what is the heat capacity of the water
C. How much heat is gained by the glass ball
D. What is the heat capacity of the glass ball
E. what is the ratio of the heat capacities of the water and the glass ball
F. What is the ratio of the temp changes of the water and glass ball
G. How are the answers to e and f related


A thermodynamic variable may be intensive or extensive.

What are intensive variables?

The variables which are independent of size or amount of substance are called intensive variables. 

Example: Density is an intensive variable. (because it does not depend on the amount of that substance)

What are extensive variables?

The variables which depend on the size or amount of the substance are called extensive variables. It is additive for independent, noninteracting subsystems

Example: Mass and volume are extensive variables. (Because they are directly measuring the amount of substance)

Thermal Expansion Problem

Meenu asked:

A metre scale is calibrated at 0 degree celsius to give correct reading. Find the distance between 50 cm and 51 cm if the scale is used at 10 degree celsius. Coefficient of linear expansion of steel is 1.1×10-5

Answers given in two books are 1.00011cm and 0.99988 why this contradiction?

(The question is being posted at PhysicsForum.PlusTwoPhysics.com too so that visitors can readily reply with their answers and explanations)

Specific Heat capacity and Molar specific Heat capacity

Chaitanya asked:

“how to calculate molar the heat capacity of a gas
given cp and cv of the gas?”



Specific heat capacity of a substance is the quantity of heat required to raise the temperature of 1g of that substance through 1oC. It can be measured at constant pressure (Cp) and at constant volume (Cv).

Molar heat capacity of a substance is the quantity of heat required to raise the temperature of 1 mole of the substance by 1oC.

Molar heat capacity = Specific heat capacity × Molecular weight,


Cv = cv × M and Cp = cp × M.


A Problem from Specific Heat of Gases

Priyanshi Gaur posted”:

“A sample of air weighing 1.18g occupies 1000 cubic cm when kept at 300 K at 1000000 Pa.When 2 cal of heat is added to it at constant volume, its temperature increases by 1 degree celcius.Calculate the amount of heat needed to increase the temperature of air by 1 degree celcius at constant pressure if the mechanical equivalent of heat is 4.2*10000000 erg/cal.”


Remember that

Cp/Cv = γ


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