Thermodynamics – JEE First

Heat transferred along two paths

April 10th, 2022jeefirst0 Comments

JEE Advanced 2014 Paper 1, Question 20

A thermodynamic system is taken from an initial state $i$ with internal energy $U_{i} = 100 \, {\rm J}$ to the final state $f$ along two different paths $i a f$ and $i b f$ , as schematically shown in the figure. The work done by the system along the paths $a f, i b$ and $b f$ are $W_{a f} = 200 \, {\rm J}, W_{i b} = 50 \, {\rm J}$ and $W_{b f} = 100 \, {\rm J}$ respectively. The heat supplied to the system along the path $i a f, i b$ and $b f$ are $Q_{i a f}, Q_{i b}$ and $Q_{b f}$ respectively. If the internal energy of the system in the state $b$ is $U_{b} = 200 \, {\rm J}$ and $Q_{i a f} = 500 \, {\rm J}$ , the ratio $Q_{b f}/Q_{i b}$ is

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Solution

The problem gives us partial information about internal energies, heat transferred, and work done at various points in the PV diagram. We …

An adiabatic bubble

April 1st, 2022jeefirst0 Comments

IIT-JEE 2008 Paper 1, Question 38,39,40

A small spherical monoatomic ideal gas bubble $\left(\gamma=\frac{5}{3}\right)$ is trapped inside a liquid of density $\rho_{\ell}$ (see figure below). Assume that the bubble does not exchange any heat with the liquid. The bubble contains $n$ moles of gas. The temperature of the gas when the bubble is at the bottom is $T_{0}$ , the height of the liquid is $H$ and the atmospheric pressure is $P_{0}$ (Neglect surface tension).

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1. As the bubble moves upwards, besides the buoyancy force the following forces are acting on it

Only the force of gravity
The force due to gravity and the force due

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Ideal gas match list

March 26th, 2022jeefirst0 Comments

JEE Advanced 2017 Paper 2, Question 16, 17 and 18

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 state 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 $n$ .

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Cyclic processes on a PV diagram

March 22nd, 2022jeefirst0 Comments

JEE Advanced 2013 Paper 2, Question 20

One mole of a monatomic ideal gas is taken along two cyclic processes $E \rightarrow F \rightarrow G \rightarrow E$ and $E \rightarrow F \rightarrow H \rightarrow E$ as shown in the PV diagram. The processes involved are purely isochoric, isobaric, isothermal or adiabatic.

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Match the paths in List I with the magnitudes of the work done in List II and select the correct answer using the codes given below the lists.

$G \to E$
$G \to H$
$F \to H$
$F \to G$

$160 P_0 V_0 \ln 2$
$36 P_0 V_0$
$24 P_0 V_0$
$31 P_0 V_0$

Codes:

$\begin{equation*} \begin{matrix} & {\rm P} & {\rm Q} & {\rm R} & {\rm S} \\ {\rm (A)} & 4 & 3 & 2 & 1 \\ {\rm (B)} & 4 & 3 & 1 & 2 \\ {\rm (C)} & 3 & 1 & 2 & 4 \\ {\rm (D)} & 1 & 3 & 2 & 4 \end{matrix} \end{equation*}$

Thermodynamic processes on an ideal gas

March 19th, 2022jeefirst0 Comments

In this note we discuss isothermal, adiabatic, isobaric, and isochoric processes with an ideal gas. We begin by recalling a few basic principles from thermodynamics, and their application to a container of ideal gas, as shown in the figure below.

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When the gas is at an absolute temperature $T > 0$ , the molecules of the gas move around inside the container and bounce off its walls. Each gas molecule suffers a change in momentum upon such a collision, and the totality of all those collisions per unit time exerts a force on the walls of the container. …