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,

& \Delta U={{q}_{v}}+W \\\ & \Delta U={{q}_{v}}+0 \\\ & \Delta U={{q}_{v}} \\\ \end{aligned}$$ Coming to given options, option B, $$-\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.