Question

The specific heat of helium at constant volume is $12.6\,Jmo{l^{ - 1}}{K^{ - 1}}$ . The specific heat of helium at constant pressure, in $Jmo{l^{ - 1}}{K^{ - 1}}$ is about: (Assume the temperature of the gas is moderate and universal gas constant, $R = 8.314\,Jmo{l^{ - 1}}{K^{ - 1}}$ )
A. $12.6$
B. $16.8$
C. $18.9$
D. $21$

Answer 1

Hint:Here we have to use the concept of specific heat and specific heat capacity. The specific heat is the quantity of heat needed per unit mass to increase the temperature by one degree Celsius. The specific heat capacity of a material in thermodynamics is the heat capacity of a sample of a substance, separated by the mass of the sample.

Complete step by step answer:
Heat, also called thermal energy, is a source of energy. Energy can be converted from one form to another a blender converts electricity into mechanical energy), but it can neither be produced nor destroyed; energy is conserved instead. The higher the temperature of a substance in simple thermodynamics, the more thermal energy it possesses. Furthermore the more of a given substance, the more overall thermal energy the material can possess at a given temperature.
Specific heat values can be calculated as follows: as two materials are put in contact with each other, each initially at a different temperature, heat often flows from the warmer material into the colder material before all materials reach the same temperature. The heat obtained by the initially colder material must match the heat lost by the initially warmer material, according to the law of energy conservation.
By calculating how much heat energy is required to lift one gram of a substance one degree Celsius, specific heat capacity is determined.
Given,
Constant volume,${C_v} = 12.6\,Jmo{l^{ - 1}}{K^{ - 1}}$, Universal gas constant,$R = 8.314\,Jmo{l^{ - 1}}{K^{ - 1}}$
We know that,
$
{C_p} = {C_v} + R \\
\Rightarrow{C_p} = 12.6 + 8.314 \\
\therefore{C_p} = 21\,Jmo{l^{ - 1}}{K^{ - 1}} \\
$
Hence, option D is the answer.

Note:We should not be confused between heat capacity and specific heat capacity. The heat used to increase the temperature of a material by one degree Celsius is the specific heat capacity. Similarly, the ratio of the energy supplied to a material and the resulting rise in its temperature is heat capacity.