If $\Delta \mathrm{U}$ and $\Delta \mathrm{W}$ represent the increase in internal energy and work done by the system respectively in a thermodynamical process, which of the following is true?

• Correct answer
  A

  $\Delta \mathrm{U}=-\Delta \mathrm{W}$, in a adiabatic process
• B

  $\Delta \mathrm{U}=\Delta \mathrm{W}$, in a isothermal process
• C

  $\Delta \mathrm{U}=\Delta \mathrm{W}$, in a adiabatic process
• D

  $\Delta \mathrm{U}=-\Delta \mathrm{W}$, in a isothermal process

Hence, the correct answer is option: 'A'.