A lab sample of gas is taken through cycle a b c a shown in...

A lab sample of gas is taken through cycle $a b c a$ shown in the $p-V$ diagram of Fig. $18-43 .$ The net work done is $+1.2 \mathrm{J}$ . Along path $a b,$ the change in the internal energy is $+3.0 \mathrm{J}$ and the magnitude of the work done is 5.0 $\mathrm{J}$ . Along path $c a,$ the energy transferred to the gas as heat is $+2.5$ J. How much energy is transferred as heat along (a) path $a b$ and (b) path $b c ?$

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Key Concepts

First Law of Thermodynamics

This principle states that the energy of an isolated system is conserved. In any process, the change in the internal energy (?U) of the system is equal to the heat (Q) added to the system minus the work (W) done by the system. Mathematically, it is expressed as ?U = Q - W. This concept is fundamental when analyzing any thermodynamic process as it relates heat transfer, work done, and changes in internal energy.

Thermodynamic Cycles

A thermodynamic cycle is a sequence of processes where the system eventually returns to its initial state, meaning that the net change in internal energy over the complete cycle is zero. In such cycles, the net heat transfer into the system must equal the net work done by the system. Understanding cyclic processes is crucial when analyzing work and heat exchanges over different stages of the cycle.

Work and Heat Sign Conventions

Correctly applying sign conventions is essential in thermodynamics. Typically, work is considered positive when done by the system and heat is positive when transferred into the system. Conversely, work done on the system and heat leaving the system are taken as negative. These conventions help in accurately computing energy exchanges during both individual processes and complete cycles.

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