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If $\Delta U$ and $\Delta W$ represent the increase in internal energy and work done by the system respectively in a thermodynamical process, which of the following is true?
A
$\Delta U = -\Delta W$, in an isothermal process
B
$\Delta U = -\Delta W$, in an adiabatic process
C
$\Delta U = \Delta W$, in an isothermal process
D
$\Delta U = \Delta W$, in an adiabatic process
Detailed Solution
First law of thermodynamics: $\Delta Q = \Delta U + \Delta W$
In an adiabatic process no heat is exchanged: $\Delta Q = 0$
$0 = \Delta U + \Delta W$, so $\Delta U = -\Delta W$
In an isothermal process of an ideal gas the temperature is constant, so $\Delta U = 0$ and $\Delta Q = \Delta W$; neither isothermal relation given is true.
Hence $\Delta U = -\Delta W$ in an adiabatic process.
In an adiabatic process no heat is exchanged: $\Delta Q = 0$
$0 = \Delta U + \Delta W$, so $\Delta U = -\Delta W$
In an isothermal process of an ideal gas the temperature is constant, so $\Delta U = 0$ and $\Delta Q = \Delta W$; neither isothermal relation given is true.
Hence $\Delta U = -\Delta W$ in an adiabatic process.