A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The rational between temperature and volume for the process is $TV^x =$ constant, then $x$ is

An ideal gas at ${27^o}C$ is compressed adiabatically to $\frac{8}{{27}}$ of its original volume. If $\gamma = \frac{5}{3}$, then the rise in temperature is........ $K$

Three samples of the same gas $A, B$ and $C(\gamma = 3/2)$ have initially equal volume. Now the volume of each sample is doubled. The process is adiabatic for $A$ isobaric for $B $ and isothermal for $C$. If the final pressures are equal for all three samples, the ratio of their initial pressures are

Which is the correct statement

An ideal monoatomic gas expands to twice its volume. If the process is isothermal, the magnitude of work done by the gas is $W_i$. If the process is adiabatic, the magnitude of work done by the gas is $W_a$. Which of the following is true?

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of  $\frac{{{C_P}}}{{{C_V}}}$  for the gas is