One mole of an ideal gas $(C_p/C_v = \gamma )$ at absolute temperature $T_1$ is adiabatically compresses from an initial pressure $P_1$ to a final pressure $P_2$. The resulting temperature $T_2$ of the gas is given by
One mole of an ideal gas $(C_p/C_v = \gamma )$ at absolute temperature $T_1$ is adiabatically compresses from an initial pressure $P_1$ to a final pressure $P_2$. The resulting temperature $T_2$ of the gas is given by
- A
${T_{_2}} = {T_1}{\left( {\frac{{{P_2}}}{{{P_1}}}} \right)^{\frac{\gamma }{{\gamma - 1}}}}$
- B
${T_{_2}} = {T_1}{\left( {\frac{{{P_2}}}{{{P_1}}}} \right)^{\frac{{\gamma - 1}}{\gamma }}}$
- C
${T_{_2}} = {T_1}{\left( {\frac{{{P_2}}}{{{P_1}}}} \right)^\gamma }$
- D
${T_{_2}} = {T_1}{\left( {\frac{{{P_2}}}{{{P_1}}}} \right)^{\gamma - 1}}$
Similar Questions
An insulated box containing a diatomic gas of molar mass $m$ is moving with velocity $v$. The box is suddenly stopped. The resulting change in temperature is :-
An insulated box containing a diatomic gas of molar mass $m$ is moving with velocity $v$. The box is suddenly stopped. The resulting change in temperature is :-
A carnot engine having an efficiency of $\frac{1}{10}$ is being used as a refrigerator. If the work done on the refrigerator is $10 \;\mathrm{J},$ the amount of heat absorbed from the reservoir at lower temperature is .............. $\mathrm{J}$
A carnot engine having an efficiency of $\frac{1}{10}$ is being used as a refrigerator. If the work done on the refrigerator is $10 \;\mathrm{J},$ the amount of heat absorbed from the reservoir at lower temperature is .............. $\mathrm{J}$
An ideal monoatomic gas is taken round the cycle $ABCDA$ shown in the $PV$ diagram in the given fig. The work done during the cycle is
An ideal monoatomic gas is taken round the cycle $ABCDA$ shown in the $PV$ diagram in the given fig. The work done during the cycle is
In the indicator diagram (in figure), net amount of work done will be
In the indicator diagram (in figure), net amount of work done will be
Given diagram shows an ideal gas taken from state $1$ to $2$ through optional paths, $A,B,C.$ Let $Q,W$ and $U$ represent the heat supplied to, the work done by gas and the internal energy of the gas, respectively. Then which of the following conditions is true?
Given diagram shows an ideal gas taken from state $1$ to $2$ through optional paths, $A,B,C.$ Let $Q,W$ and $U$ represent the heat supplied to, the work done by gas and the internal energy of the gas, respectively. Then which of the following conditions is true?