For an isothermal process:
A. $dQ{\text{ }} = {\text{ }}dW$
B. $dQ{\text{ }} = {\text{ }}dU$
C. $dW{\text{ }} = {\text{ }}dU$
D. $dQ{\text{ }} = {\text{ }}dU{\text{ }} + {\text{ }}dW$

Hint: In the given question we will be dealing with the concepts of thermodynamics. Now, as we know that thermodynamics deals with the idea of heat and temperature and the inter-conversion of heat and other forms of energy.

Complete answer:
In physics thermodynamics is the branch which deals with heat, work and temperature, and their relation to energy, radiation and physical properties of matter. In other words, it describes the process of conversion of how thermal energy gets converted to or gets converted from other forms of the energy, and how matter gets affected by this process.
Thermodynamics is governed by four laws, which are:
1) Zeroth law: If two systems are both in thermal equilibrium with a third system, then they are in thermal equilibrium with each other
2) First law: When energy moves into or out of a system, the system’s internal energy changes in accordance with the law of conservation of mass.
3) Second law: The state of the entropy of the entire universe, as an isolated system, will always increase over time.
4) Third law: Entropy of a perfect crystal at absolute zero is zero.
Isothermal process is defined as a thermodynamic process in which the temperature of the system remains constant, and the transfer of heat in or out of the system occurs so slowly that thermal equilibrium is maintained.
Internal energy is a function of temperature. So, in an isothermal process, it will be constant.
According to the First Law of Thermodynamics,
$dQ{\text{ }} = {\text{ }}dU{\text{ }} + {\text{ }}dW$
Here, $dU{\text{ }} = {\text{ }}0$
$\therefore dQ{\text{ }} = {\text{ }}dW$
Thus, for an isothermal process $dQ{\text{ }} = {\text{ }}dW$.
Hence, option (A) is the correct answer.

Note:
In this question we talked about isothermal process similarly there are more thermodynamic processes other than that having different properties, such as:
Isobaric process: It is a process in which there is no change in pressure.
Isochoric: It is a process in which there is no change in the volume.
Adiabatic process: It is a process in which there is no heat transfer in or out of the system.