$A$ 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$83$
Explore More
Similar Questions
One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is $4 \text{ cm}^2$. The gas is heated slowly to raise the temperature by $1.2^\circ\text{C}$ during which the piston moves by $25 \text{ mm}$. The amount of heat supplied to the gas is . . . . . . $J$. (Atmospheric pressure = $100 \text{ kPa}$, $R = 8.3 \text{ J/mol}\cdot\text{K}$) (Neglect mass of the piston)
DifficultJEE MAIN 2026
View SolutionFill in the blanks:
$1.$ The heat required to raise the temperature of a body by $1\,K$ is called ...... .
$2.$ $A$ temperature difference of $10\,^{\circ}C$ is equivalent to a temperature difference of ...... on the Fahrenheit temperature scale.
$3.$ For an isothermal process of an ideal gas,$\frac{dP}{P} = .........$
$1.$ The heat required to raise the temperature of a body by $1\,K$ is called ...... .
$2.$ $A$ temperature difference of $10\,^{\circ}C$ is equivalent to a temperature difference of ...... on the Fahrenheit temperature scale.
$3.$ For an isothermal process of an ideal gas,$\frac{dP}{P} = .........$
Medium
View SolutionWhich of the following is correct in terms of increasing work done for the same initial and final state?
Medium
View SolutionOne mole of a monatomic ideal gas undergoes the cyclic process $J \rightarrow K \rightarrow L \rightarrow M \rightarrow J$,as shown in the $P - T$ diagram. Match the quantities mentioned in $List-I$ with their values in $List-II$ and choose the correct option. [$R$ is the gas constant]
$List-I$ $List-II$ $(P)$ Work done in the complete cyclic process $(1)$ $R T_0 - 4 R T_0 \ln 2$ $(Q)$ Change in the internal energy of the gas in the process $JK$ $(2)$ $0$ $(R)$ Heat given to the gas in the process $KL$ $(3)$ $3 R T_0$ $(S)$ Change in the internal energy of the gas in the process $MJ$ $(4)$ $-2 R T_0 \ln 2$ $(5)$ $-3 R T_0 \ln 2$
| $List-I$ | $List-II$ |
| $(P)$ Work done in the complete cyclic process | $(1)$ $R T_0 - 4 R T_0 \ln 2$ |
| $(Q)$ Change in the internal energy of the gas in the process $JK$ | $(2)$ $0$ |
| $(R)$ Heat given to the gas in the process $KL$ | $(3)$ $3 R T_0$ |
| $(S)$ Change in the internal energy of the gas in the process $MJ$ | $(4)$ $-2 R T_0 \ln 2$ |
| $(5)$ $-3 R T_0 \ln 2$ |
Two cylinders $A$ and $B$ fitted with pistons contain an equal amount of an ideal diatomic gas at temperature $T$ $K$. The piston of cylinder $A$ is free to move,while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $dT_{A}$,then the rise in temperature of the gas in cylinder $B$ is (where $\gamma = \frac{C_{P}}{C_{V}}$):
DifficultMHT CET 2024
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo