Question

Mathematical equation of first law of thermodynamics for isochoric process is:
a.) \[\Delta U={{q}_{v}}\]
b.) \[-\Delta U={{q}_{v}}\]
c.) \[q=-W\]
d.) \[\Delta U=W\]

Answer 1

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.