Question

state first law of thermodynamics. why c p is greater than c v. proove c p - c v = r

Answer 1

The First Law of Thermodynamics states that heat is a form of energy, andthermodynamic processes are therefore subject to the principle of conservation of energy. This means that heat energy cannot be created or destroyed.
Why is CP greater than CV in thermodynamics?


Heat capacity is the heat required to raise the temperature of the system by one degree. Unit of heat capacity is J/K in SI unit system.

When heat capacity is expressed on a unit mass basis, then it is called specific heat. The unit of specific heat is J/kg.K

Cp = heat capacity at constant pressure

Cv = heat capacity at constant volume

Constant volume indicates that there is no change in volume. Therefore the only change in the system is internal energy of the system, due to the addition of heat.

Constant pressure heat capacity is where some amount of heat is also required for the expansion process(change in volume).

Relation between CP and CV in gaseous systems

No external work is being done when a gas is heated at constant volume i.e. gas uses all the haet which is given to it for increasing its internal energy. Hence if temperature of one mole of a gas is raised through 1oC, the molar heat capacity is given itself at constant volume by increase in internal energy.

But when a gas is heated at constant pressure there will be expansion of gas i.e. increase in volume take place and some external work will b done. For this some extra heat is required which should be given to the gas to perform the external work.

Hence the Molar Heat capacity of a gas at constant pressure must be greater than Molar Heat capacity of a gas at constant volume.
CP > CV

When gas is heated through 1oC at constant pressure, the difference between these will give the work done by one mole of the gas in expansion.

As we know that at constant pressure work done by gas in expansion is given mathematically as:

w= P∆V
For one mole of an ideal gas:
PV = RT ……………………….. (1)
When temperature is raised by 1oC from T to T + 1 so that volume becomes V + ∆V, then

P (V + ∆V) = R (T +1) ………………………………… (2)

Subtracting equation (1) from equation (2), we get:
P∆V = R

Thus, At constant pressure work done by one mole of the an ideal gas in expansion when heated through 1oC is equal to R. hence,

CP – CV = R

Thus, the difference between molar heat capacity of a gas at constant pressure, CP and at constant volume, CV is equal to the gas constant R. i.e. 1.987 cal or 8.314 J

Answer 2

Answer:

more heat is required to increase the temperature of gas in the first case! Therefore, CP, or specific heat at constant pressure is more than CV, or specific heat at constant volume, since it takes more heat to increase the temperature by one unit in the former case.