If $C_p$ and $C_v$ denote the specific heat of nitrogen at constant pressure and constant volume respectively,then

What is the relationship between the internal energy $U$ of an ideal gas and its pressure $P$ and volume $V$?

To increase the temperature of $1$ $mol$ of an ideal gas by $10$ $K$ at constant pressure,$207$ $J$ of heat is required. If the temperature of this gas is increased by $10$ $K$ at constant volume,the heat required is ....... $J$ $(R = 8.3$ $J/mol$ $K)$.

The specific heat of a gas at constant volume is $21.2 \, J/mol/^{\circ}C$. If the temperature is increased by $1^{\circ}C$ keeping the volume constant,the change in its internal energy will be ...... $J$.

For hydrogen gas,$C_P - C_V = a$,and for oxygen gas,$C_P - C_V = b$. The relationship between $a$ and $b$ is given by: (where $C_P$ and $C_V$ are molar specific heats at constant pressure and constant volume,respectively.)

Which of the following statements is correct?