Question

The area under the plot ${{C}_{p}}/T$ versus the absolute temperature (T) is directly related to
(A) $\Delta S$
(B) $\Delta U$
(C) $\Delta H$
(D) q

Answer 1

${{C}_{p}}$ stands for critical pressure. Which is the pressure is defined as the pressure above the liquid and the gas can not coexist at any temperature. The critical temperature for a pure substance is defined as the temperature above which the gas cannot exist as liquid regardless of the applied pressure.

Complete Answer:
In thermodynamics entropy is generally referred to as a measurement of the spontaneous changes which occurs in a system. In the thermodynamic system entropy is referred to as S. the certain characteristics of entropy is that the value of entropy depends upon the amount of substance present in the system. Hence entropy is an extensive property. Value of entropy is dependent upon the amount of substances which are present in the system. Change in the value of entropy depends on the change in quantities such as temperature, volume, pressure and the number of moles of the system. The area under the plot ${{C}_{p}}/T$ versus the absolute temperature (T) is directly related to entropy.

Hence the correct answer is option (B) i.e. $\Delta S$

Note: Since it is difficult and practically impossible to determine the actual total entropy content of a system, it is described as the change in entropy accompanying the change in the state of the system. The SI unit is J/Kmol and in the CGS unit it is cal/Kmol. Entropy describes the behavior of a system in the terms of temperature, pressure and heat capacity.