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(D) For a complete thermodynamic cycle,the change in internal energy is zero,so $\Delta U_{cycle} = \Delta U_{1\rightarrow 2} + \Delta U_{2\rightarrow

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(D) For a complete thermodynamic cycle,the change in internal energy is zero,so $\Delta U_{cycle} = \Delta U_{1\rightarrow 2} + \Delta U_{2\rightarrow 3} + \Delta U_{3\rightarrow 1} = 0$. Given: $\Delta U_{2\rightarrow 3} = -20\,J$ (decrease in internal energy). For process $3\rightarrow 1$ (adiabatic),$Q_{3\rightarrow 1} = 0$. From the first law of thermodynamics,$\Delta U_{3\rightarrow 1} = Q_{3\rightarrow 1} - W_{3\rightarrow 1}$. Work done on the system is $20\,J$,so $W_{3\rightarrow 1} = -20\,J$. Thus,$\Delta U_{3\rightarrow 1} = 0 - (-20\,J) = 20\,J$. Now,$\Delta U_{1\rightarrow 2} + (-20\,J) + 20\,J = 0$,which gives $\Delta U_{1\rightarrow 2} = 0$. Total work done in the cycle $W_{cycle} = W_{1\rightarrow 2} + W_{2\rightarrow 3} + W_{3\rightarrow 1} = 10\,J$. Since process $2\rightarrow 3$ is isochoric,$W_{2\rightarrow 3} = 0$. So,$W_{1\rightarrow 2} + 0 + (-20\,J) = 10\,J$,which gives $W_{1\rightarrow 2} = 30\,J$. For process $1\rightarrow 2$ (isothermal),$\Delta U_{1\rightarrow 2} = 0$. Applying the first law: $Q_{1\rightarrow 2} = \Delta U_{1\rightarrow 2} + W_{1\rightarrow 2} = 0 + 30\,J = 30\,J$.

List-$I$	List-$II$
$(A)$ Isothermal	$(I)$ $\Delta W = 0$
$(B)$ Adiabatic	$(II)$ $\Delta Q = 0$
$(C)$ Isobaric	$(III)$ $\Delta U \neq 0$
$(D)$ Isochoric	$(IV)$ $\Delta U = 0$

Column-$I$	Column-$II$
$(i)$ Adiabatic process	$(a)$ Constant temperature
$(ii)$ Isolated system	$(b)$ No exchange of energy and matter
$(iii)$ Isothermal change	$(c)$ First law of thermodynamics
$(iv)$ Law of conservation of energy	$(d)$ No transfer of heat only

Similar Questions

Match List-$I$ with List-$II$.
List-$I$ List-$II$
$(A)$ Isothermal $(I)$ $\Delta W = 0$
$(B)$ Adiabatic $(II)$ $\Delta Q = 0$
$(C)$ Isobaric $(III)$ $\Delta U \neq 0$
$(D)$ Isochoric $(IV)$ $\Delta U = 0$

Choose the correct answer from the options given below:

Which of the following quantities does not characterize the thermodynamic state of a substance?

Two gases have the same initial pressure,volume,and temperature. They expand to the same final volume,one adiabatically and the other isothermally. Which of the following statements is correct regarding the final state?

Match the following $:-$

Column-$I$ Column-$II$

$(i)$ Adiabatic process $(a)$ Constant temperature

$(ii)$ Isolated system $(b)$ No exchange of energy and matter

$(iii)$ Isothermal change $(c)$ First law of thermodynamics

$(iv)$ Law of conservation of energy $(d)$ No transfer of heat only

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