Thus the “15° calorie” (also called the gram-calorie, or small calorie) was defined as the amount of heat that will raise the temperature of 1 gram of water from 14.5° to 15.5° C—equal to 4.1855 joules.

Q can be used to determine which direction a reaction will shift to reach equilibrium. If K > Q, a reaction will proceed forward, converting reactants into products. If K < Q, the reaction will proceed in the reverse direction, converting products into reactants. If Q = K then the system is already at equilibrium.

In equation form, the first law of thermodynamics is ΔU = Q − W. Here ΔU is the change in internal energy U of the system. Q is the net heat transferred into the system—that is, Q is the sum of all heat transfer into and out of the system.

The specific heat of gas at constant volume in terms of degree of freedom ‘f’ is given as: Cv = (f/2) R. So, we can also say that, Cp/Cv = (1 + 2/f), where f is degree of freedom. Monoatomic gas has only one translational motion, hence three translational degrees of freedom.

In Section 8.1 we pointed out that the heat capacity at constant pressure must be greater than the heat capacity at constant volume. We also showed that, for an ideal gas, CP = CV + R, where these refer to the molar heat capacities.

Considering the classical formula: Cp = Cv + R , and knowing R is P(deltaV/deltaT)p , For solids which are incompressible; deltaV term is zero. Thus R is zero. Thus Cp = Cv .

1a: cp – cv = R. where cp is the specific heat coefficient at constant pressure, cv is the the specific heat coefficient at constant volume, gamma is the ratio of specific heats, and R is the gas constant from the equation of state.

The molar specific heat of a gas at constant pressure (Cp) is the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant pressure. Its value for monatomic ideal gas is 5R/2 and the value for diatomic ideal gas is 7R/2.

The heat capacity at constant pressure can be estimated because the difference between the molar Cp and Cv is R; Cp – Cv = R. Although this is strictly true for an ideal gas it is a good approximation for real gases.

The nominal values used for air at 300 K are CP = 1.00 kJ/kg. K, Cv = 0.718 kJ/kg.

Hint: The isothermal expansion means a gas is expanding from initial volume to final volume at constant temperature. The internal energy and enthalpy depend upon the temperature only in case of ideal gas. So, during the isothermal expansion of an ideal gas, the temperature remains constant and volume increases.

If the gas is ideal, the amount of energy entering the environment is equal to the work done on the gas, because internal energy does not change. If there is also no work done, i.e. a free expansion, there is no change in internal energy. For an ideal gas, this means that the process is also isothermal.

The isothermal approach is used to enhance the heat transfer of compressed air to maintain the temperature constant as the environment. Two main methods to achieve isothermal compression are to inject the liquid spray or foam into the compression chamber and liquid piston.