Question

The value of \[{C_P} - {C_V} = 1.06R\] for a gas sample in state A and is \[1.00R\] in state B. Let \[{T_A} and {T_B}\] denote the temperature \[{P_A}and{P_B}\] denote the pressure of the state A and B respectively. Then:
(A) \[{P_A} < {P_B} \ and \ {T_A} > {T_B}\]
(B) \[{P_A} > {P_B }\ and \ { T_A} > {T_B}\]
(C) \[{P_A} = {P_B} \ and \ {T_A} = {T_B}\]
(D) \[{P_A} > {P_B} \ and \ {T_A} < {T_B}\]

Answer 1

Hint: Heat term related to thermodynamics. In thermodynamics we deal with how much heat is produced or released during a chemical reaction and forms of energy (heat is a form of energy) and how energy is converted into other forms.

Complete step by step answer:
When a body or element absorbs heat in our body then the temperature of the body is automatically increased and the heat is converted into Kinetic energy. And kinetic energy may be defined as the energy that is required to move the particles.
Heat is directly proportional to the number of moles because if the number of moles more of any gas or molecules then more heat is required to raise the temperature of the body.
So Heat is directly proportional to number of moles of substance as well as change in temperature between products and reactants.
\[q \propto n\Delta T\]
\[q = Cm\Delta T\]
Here C is constant known as molar heat capacity.
For state A-\[{C_P} - {C_V} = 1.06R\]
 It means this gas does not behave as ideal gas, this gas behaves as real gas. And real gas does not obey thermodynamics gas law.
For state B- \[{C_P} - {C_V} = 1.00R\]
\[{C_P} - {C_V} = R\]
It means this gas behaves as an ideal gas. It means this gas obeys all thermodynamics gas laws.
Any gas behave as ideal at high temperature and low pressure
Hence, option A is the correct option. So, \[{P_A} < {P_B} \ and \ {T_A} > {T_B}\] this condition is followed by gas A and gas B.

Note: Ideal gas is a gas that at all temperature and pressure follow all thermodynamics gas laws. Real gas is a gas that at all temperature and pressure does not follow all thermodynamics gas laws. Ideal gas is that gas which consists of very large numbers of particles of gases. No ideal gas is present in nature and all gases present in nature behave as real gas.