Two gases have the same initial pressure, volume and temperatue. They expand to the same final volume, one adiabatically and the other isothermally
Two gases have the same initial pressure, volume and temperatue. They expand to the same final volume, one adiabatically and the other isothermally
- A
The final temperature is greater for the isothermal process
- B
The final pressure is greater for the isothermal process
- C
The work done by the gas is greater for the isothermal process
- D
All of the above
Similar Questions
A gas is suddenly compressed to one fourth of its original volume. What will be its final pressure, if its initial pressure is $P$
A gas is suddenly compressed to one fourth of its original volume. What will be its final pressure, if its initial pressure is $P$
A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas, with specific heat at constant volume, $C_v=2 R$. Here, $R$ is the gas constant. Initially, each side has a volume $V_0$ and temperature $T_0$. The left side has an electric heater, which is turned on at very low power to transfer heat $Q$ to the gas on the left side. As a result the partition moves slowly towards the right reducing the right side volume to $V_0 / 2$. Consequently, the gas temperatures on the left and the right sides become $T_L$ and $T_R$, respectively. Ignore the changes in the temperatures of the cylinder, heater and the partition.
($1$) The value of $\frac{T_R}{T_0}$ is
$(A)$ $\sqrt{2}$ $(B)$ $\sqrt{3}$ $(C)$ $2$ $(D)$ $3$
($2$) The value of $\frac{Q}{R T_0}$ is
$(A)$ $4(2 \sqrt{2}+1)$ $(B)$ $4(2 \sqrt{2}-1)$ $(C)$ $(5 \sqrt{2}+1)$ $(D)$ $(5 \sqrt{2}-1)$
Give the answer or qution ($1$) and ($2$)
A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas, with specific heat at constant volume, $C_v=2 R$. Here, $R$ is the gas constant. Initially, each side has a volume $V_0$ and temperature $T_0$. The left side has an electric heater, which is turned on at very low power to transfer heat $Q$ to the gas on the left side. As a result the partition moves slowly towards the right reducing the right side volume to $V_0 / 2$. Consequently, the gas temperatures on the left and the right sides become $T_L$ and $T_R$, respectively. Ignore the changes in the temperatures of the cylinder, heater and the partition.
($1$) The value of $\frac{T_R}{T_0}$ is
$(A)$ $\sqrt{2}$ $(B)$ $\sqrt{3}$ $(C)$ $2$ $(D)$ $3$
($2$) The value of $\frac{Q}{R T_0}$ is
$(A)$ $4(2 \sqrt{2}+1)$ $(B)$ $4(2 \sqrt{2}-1)$ $(C)$ $(5 \sqrt{2}+1)$ $(D)$ $(5 \sqrt{2}-1)$
Give the answer or qution ($1$) and ($2$)
- [IIT 2021]
The slopes of isothermal and adiabatic curves are related as
The slopes of isothermal and adiabatic curves are related as
One mole of an ideal gas $(\gamma = 1.4)$ is adiabatically compressed so that its temperature rises from $27\,^oC$ to $35\,^oC$. The change in the internal energy of the gas is .... $J$ (given $R = 8.3 \,J/mole/K$)
One mole of an ideal gas $(\gamma = 1.4)$ is adiabatically compressed so that its temperature rises from $27\,^oC$ to $35\,^oC$. The change in the internal energy of the gas is .... $J$ (given $R = 8.3 \,J/mole/K$)
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]