Heat transferred along two paths

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

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An adiabatic bubble

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

  1. Only the force of gravity
  2. The force due to gravity and the force due
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Ideal gas match list

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

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.

  1. G \to E
  2. G \to H
  3. F \to H
  4. F \to G
  1. 160 P_0 V_0 \ln 2
  2. 36 P_0 V_0
  3. 24 P_0 V_0
  4. 31 P_0 V_0


    \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*}

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Thermodynamic processes on an ideal gas

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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A container of ideal gas.

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. …

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