What is the mathematical expression of first law of thermodynamics for an isochoric process?

Text Solution

`DeltaU=qv``-Delta=qv``q=-W``DeltaU=W`

Answer : A

Solution : For an isochoric process, `DeltaV=0` In this process, the first law of thermodynamics `q=DeltaU-W` `q=DeltaU-PDeltaV` As `DeltaV=0` `qV=DeltaU`

Text Solution

`DeltaU = q_(v)``-DeltaU = q_(v)``q=-W``DeltaU =W`

Answer : A

Solution : `DeltaU =q,` is the mathematical equation of first law of thermodynamics for isochoric process. Because for isochoric process, `DeltaV=0 therefore W = PDeltaV=0 therefore DeltaU=q_(v)`

Answer

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Hint: “The First Law of Thermodynamics states that heat is a form of energy, and thermodynamic processes are therefore subject to the principle of conservation of energy. This means that heat energy cannot be created or destroyed”.

Complete step-by-step answer:

In the question it is given that it is an isochoric process. An isochoric process is a process in which the volume of the closed system undergoing such a process remains constant.According to first law of thermodynamics,\[\Delta U={{q}_{v}}+W\]Here \[\Delta U\]= change in internal energy, W = net work done, \[{{q}_{v}}\] = net heat transfer. In an isochoric process, the work done is zero, since there is no change in volume so work done is zero. W = 0.Therefore, \[\begin{align} & \Delta U={{q}_{v}}+W \\ & \Delta U={{q}_{v}}+0 \\ & \Delta U={{q}_{v}} \\ \end{align}\]Coming to given options, option B, \[-\Delta U={{q}_{v}}\], it is wrong because in isochoric process change in internal energy is not negative. Coming to option C, \[q=-W\], it is also because in isochoric process work is done zero.Coming to option D, \[\Delta U=W\], it is also wrong in isochoric process work done is zero so change in internal energy is equal to work done. Coming to option A, \[\Delta U={{q}_{v}}\], it is matching with the answer that we got in the above calculation. So, the correct option is A. Note: Don’t be confused with isochoric process and isobaric process. Both are not the same.Isochoric process: A process in which volume is kept constant throughout the process.Isobaric process: A process in which pressure is kept constant throughout the process.

By substituting equation `W= -p_(ex).triangleV` in the equation `triangleU=q+W`, we get

`triangleU=q-p_(ex).triangleV .........(1)`

If the reaction is carried out in a closed container so that the volume of the system is constant, then`triangleV=0.`In such a case, no work is involved.

The equation (1) becomes `triangleU=q_v.`

Equation (1) suggests that the change in internal energy of the system is due to heat transfer. The subscript v indicates a constant volume process. As U is a state function, qv is also a state function. We see that an increase in the internal energy of a system is numerically equal to the heat absorbed by the system in a constant volume (isochoric) process.