An ideal gas undergoes isothermal process from some initial state… - Vidyadip

MCQ

An ideal gas undergoes isothermal process from some initial state $i$ to final state $f.$ Choose the correct alternatives.

$\text{dU = 0}$
$\text{dQ= 0}$
$\text{dQ = dU}$
$\text{dQ = dW}$

✓
$b$ and $d$
B
$b$ and $c$
C
$a$ and $d$
D
$c$ and $d$

✓

Answer

Correct option: A.

$b$ and $d$

Key concept: First Law of Thermodynamics.
It is a statement of conservation of energy in thermodynamical process.
According to it heat given to a system $(\Delta\text{Q})$ is equal to the sum of increase in its internal energy $\text{(AIT)}$ and the work done $\text{(AW)}$ by the system against the surroundings.
$\Delta\text{Q}=\Delta\text{U}+\Delta\text{W}$
According to the first law of thermodynamics. $\Delta\text{A}\text{Q}=\Delta\text{U}+\Delta\text{W}$ but
$\Delta\text{U}\propto\Delta\text{T}$
$\Delta\text{U}=0[\text{As } \Delta\text{T}=0]$
$\Delta\text{Q}=\Delta\text{W}$,
i.e., heat supplied in an isothermal change is used to do work against external surrounding or if the work is done on the system then equal amount of heat energy will be liberated by the system

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