1. Tardigrade
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  3. Chemistry
  4. Which of the following expressions is true for an ideal gas?

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Q. Which of the following expressions is true for an ideal gas?

Thermodynamics

Solution:

(a) From charle's law: $V \propto T$
$\Rightarrow V=k_1 T $ (at cons. P)
$\Rightarrow\left(\frac{d V}{d T}\right)_P=k_1 \neq 0$
(b) From GayLussac's law:
$P \propto T $ (at cons. $V$ )
$\Rightarrow P = K _2 T$
$\Rightarrow\left(\frac{d P}{d T}\right)_V=k_2 \neq 0$
(c) For an ideal gas, change in internal energy is zero at constant temperature. $(d U)_T=0$
$\Rightarrow\left(\frac{d U}{d V}\right)_T=0$
(d) $\Delta U =n C_V \Delta T $ (at cons. $V$ )
$\Rightarrow\left(\frac{d U}{d T}\right)_V=n C_V \neq 0$