In an adiabatic process, the state of a gas is changed from ${P_1},{V_1},{T_1} $ to ${P_2},{V_2},{T_2}$. Which of the following relation is correct
${T_1}{V_1}^{\gamma - 1} = {T_2}{V_2}^{\gamma - 1}$
${P_1}{V_1}^{\gamma - 1} = {P_2}{V_2}^{\gamma - 1}$
${T_1}{P_1}^\gamma = {T_2}{P_2}^\gamma $
${T_1}{V_1}^\gamma = {T_2}{V_2}^\gamma $
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
A sample of an ideal gas is contained in a cylinder. The volume of the gas is suddenly decreased. A student makes the following statements to explain the change in pressure of the gas
$I.$ The average kinetic energy of the gas atoms increases
$II.$ The atoms of the gas hit the walls of the cylinder more frequently
$III.$ Temperature of the gas remains unchanged
Which of these statements is true?
An ideal monoatomic gas with pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $2\, V$ and a final pressure $P_i$. If the same gas is expanded adiabatically to a volume $2\,V$, the final pressure is $P_a$ . The ratio $\frac{{{P_a}}}{{{P_i}}}$ is
If $\gamma $ denotes the ratio of two specific heats of a gas, the ratio of slopes of adiabatic and isothermal $PV$ curves at their point of intersection is
A gas is being compressed adiabatically. The specific heat of the gas during compression is