$A$ gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure $P_i = 10^5 \text{ Pa}$ and volume $V_i = 10^{-3} \text{ m}^3$ changes to a final state at $P_f = (1/32) \times 10^5 \text{ Pa}$ and $V_f = 8 \times 10^{-3} \text{ m}^3$ in an adiabatic quasi-static process, such that $P^3 V^5 = \text{constant}$. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at $P_i$, followed by an isochoric (isovolumetric) process at volume $V_f$. The amount of heat supplied to the system in the two-step process is approximately: (in $\text{ J}$)
- A$112$
- B$294$
- C$588$
- D$83$
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Match the following:
Column $I$ Column $II$ $A$. Ratio of $\frac{\Delta Q}{\Delta U}$ in an isobaric process $1$. $\frac{T_1}{T_1-T_2}$ $B$. Ratio of $\frac{\Delta Q}{\Delta W}$ in an isobaric process $2$. $\frac{T_2}{T_1-T_2}$ $C$. Coefficient of performance of a refrigerator $3$. $\frac{\gamma}{\gamma-1}$ $D$. Coefficient of performance of a heat pump $4$. $\gamma$
Codes:
$A \quad B \quad C \quad D$
| Column $I$ | Column $II$ |
| $A$. Ratio of $\frac{\Delta Q}{\Delta U}$ in an isobaric process | $1$. $\frac{T_1}{T_1-T_2}$ |
| $B$. Ratio of $\frac{\Delta Q}{\Delta W}$ in an isobaric process | $2$. $\frac{T_2}{T_1-T_2}$ |
| $C$. Coefficient of performance of a refrigerator | $3$. $\frac{\gamma}{\gamma-1}$ |
| $D$. Coefficient of performance of a heat pump | $4$. $\gamma$ |
Codes:
$A \quad B \quad C \quad D$
Match the thermodynamic processes taking place in a system with the correct conditions. In the table: $\Delta Q$ is the heat supplied,$\Delta W$ is the work done and $\Delta U$ is change in internal energy of the system.
Process Condition $(I)$ Adiabatic $(A) \Delta W = 0$ $(II)$ Isothermal $(B) \Delta Q = 0$ $(III)$ Isochoric $(C) \Delta U \neq 0, \Delta W \neq 0, \Delta Q \neq 0$ $(IV)$ Isobaric $(D) \Delta U = 0$
| Process | Condition |
| $(I)$ Adiabatic | $(A) \Delta W = 0$ |
| $(II)$ Isothermal | $(B) \Delta Q = 0$ |
| $(III)$ Isochoric | $(C) \Delta U \neq 0, \Delta W \neq 0, \Delta Q \neq 0$ |
| $(IV)$ Isobaric | $(D) \Delta U = 0$ |
Three moles of an ideal monoatomic gas perform a cycle as shown in the figure. The gas temperatures in different states are: $T_1 = 400\, K, T_2 = 800\, K, T_3 = 2400\, K$ and $T_4 = 1200\, K.$ The work done by the gas during the cycle is ........ $kJ$.
Difficult
View SolutionConsider two containers $A$ and $B$ containing monoatomic gases at the same Pressure $(P)$,Volume $(V)$ and Temperature $(T)$. The gas in $A$ is compressed isothermally to $\frac{1}{8}$ of its original volume while the gas $B$ is compressed adiabatically to $\frac{1}{8}$ of its original volume. The ratio of final pressure of gas in $B$ to that of gas in $A$ is ...........
Answer the following questions based on the $P-T$ phase diagram of $CO_{2}$:
$(a)$ $CO_{2}$ at $1 \; atm$ pressure and temperature $-60^{\circ} C$ is compressed isothermally. Does it go through a liquid phase?
$(b)$ What happens when $CO_{2}$ at $4 \; atm$ pressure is cooled from room temperature at constant pressure?
$(c)$ Describe qualitatively the changes in a given mass of solid $CO_{2}$ at $10 \; atm$ pressure and temperature $-65^{\circ} C$ as it is heated up to room temperature at constant pressure.
$(d)$ $CO_{2}$ is heated to a temperature $70^{\circ} C$ and compressed isothermally. What changes in its properties do you expect to observe?
$(a)$ $CO_{2}$ at $1 \; atm$ pressure and temperature $-60^{\circ} C$ is compressed isothermally. Does it go through a liquid phase?
$(b)$ What happens when $CO_{2}$ at $4 \; atm$ pressure is cooled from room temperature at constant pressure?
$(c)$ Describe qualitatively the changes in a given mass of solid $CO_{2}$ at $10 \; atm$ pressure and temperature $-65^{\circ} C$ as it is heated up to room temperature at constant pressure.
$(d)$ $CO_{2}$ is heated to a temperature $70^{\circ} C$ and compressed isothermally. What changes in its properties do you expect to observe?
Medium
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