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
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
- [AIPMT 2013]
- [AIEEE 2003]
- A
$2$
- B
$1.67$
- C
$1.5$
- D
$1.33$
Similar Questions
An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $P$ $V$ diagrams in column $3$ of the table. Consider only the path from state $1$ to $2 . W$ denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here $\gamma$ is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is $n$.
(image)
($1$) Which of the following options is the only correct representation of a process in which $\Delta U=\Delta Q-P \Delta V$ ?
$[A] (II) (iv) (R)$ $[B] (II) (iii) (P)$ $[C] (II) (iii) (S)$ $[D] (III) (iii) (P)$
($2$) Which one of the following options is the correct combination?
$[A] (III) (ii) (S)$ $[B] (II) (iv) (R)$ $[C] (II) (iv) (P)$ $[D] (IV) (ii) (S)$
($3$) Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in an ideal gas?
$[A] (III) (iv) (R)$ $[B] (I) (ii)$ $(\mathrm{Q})$ $[C] (IV) (ii) (R)$ $[D] (I) (iv) (Q)$
An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $P$ $V$ diagrams in column $3$ of the table. Consider only the path from state $1$ to $2 . W$ denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here $\gamma$ is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is $n$.
(image)
($1$) Which of the following options is the only correct representation of a process in which $\Delta U=\Delta Q-P \Delta V$ ?
$[A] (II) (iv) (R)$ $[B] (II) (iii) (P)$ $[C] (II) (iii) (S)$ $[D] (III) (iii) (P)$
($2$) Which one of the following options is the correct combination?
$[A] (III) (ii) (S)$ $[B] (II) (iv) (R)$ $[C] (II) (iv) (P)$ $[D] (IV) (ii) (S)$
($3$) Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in an ideal gas?
$[A] (III) (iv) (R)$ $[B] (I) (ii)$ $(\mathrm{Q})$ $[C] (IV) (ii) (R)$ $[D] (I) (iv) (Q)$
- [IIT 2017]
A balloon filled with helium $\left(32^{\circ} C \right.$ and $1.7\; atm$.) bursts. Immediately afterwards the expansion of helium can be considered as
A balloon filled with helium $\left(32^{\circ} C \right.$ and $1.7\; atm$.) bursts. Immediately afterwards the expansion of helium can be considered as
- [JEE MAIN 2020]
A monoatomic ideal gas, initially at temperature ${T_1},$ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature. ${T_2}$ by releasing the piston suddenly. If ${L_1}$ and ${L_2}$ are the lengths of the gas column before and after expansion respectively, then ${T_1}/{T_2}$ is given by
A monoatomic ideal gas, initially at temperature ${T_1},$ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature. ${T_2}$ by releasing the piston suddenly. If ${L_1}$ and ${L_2}$ are the lengths of the gas column before and after expansion respectively, then ${T_1}/{T_2}$ is given by
- [IIT 2000]
A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is $\left(\right.$ given, $\left.\gamma=\frac{3}{2}\right)$ :
A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is $\left(\right.$ given, $\left.\gamma=\frac{3}{2}\right)$ :
- [JEE MAIN 2023]
A cycle followed by an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in figure. Find heat exchanged by the engine, with the surroundings for each section of the cycle.${C_v} = \frac{3}{2}R$
$(a)$ $A$ to $B$ : constant volume
$(b)$ $B$ to $C$ : constant pressure
$(c)$ $C$ to $D$ : adiabatic
$(d)$ $D$ to $A$ : constant pressure
A cycle followed by an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in figure. Find heat exchanged by the engine, with the surroundings for each section of the cycle.${C_v} = \frac{3}{2}R$
$(a)$ $A$ to $B$ : constant volume
$(b)$ $B$ to $C$ : constant pressure
$(c)$ $C$ to $D$ : adiabatic
$(d)$ $D$ to $A$ : constant pressure