No, it is not possible for a gas to be isothermal and isochoric (constant volume) at the same time.
The term "isothermal" means that the gas is undergoing a process or in a state where its temperature remains constant. In an isothermal process, the gas exchanges heat with its surroundings to maintain a constant temperature. This implies that the gas's internal energy changes as heat is added or removed.
On the other hand, "isochoric" refers to a process or state in which the volume of the gas remains constant. In an isochoric process, no work is done by or on the gas through volume change. The gas molecules may still have kinetic energy and interact, leading to changes in pressure, but the volume remains constant.
For a gas to be isothermal, its temperature must remain constant. This requires heat exchange with the surroundings, which typically involves a change in volume. In other words, the gas needs to be able to expand or contract to maintain its temperature constant during the process.
Therefore, since an isochoric process implies a constant volume, it does not allow the gas to change its temperature by exchanging heat with the surroundings. As a result, a gas cannot be isothermal and isochoric simultaneously.