In an adiabatic process, which of the following statements is true?

In an adiabatic process, which of the following statements is true?
  1. The molar heat capacity is infinite
  2. Work done by the gas equals the increase in internal energy
  3. The molar heat capacity is zero
  4. The internal energy of the gas decreases as the temperature increases

Solution

For adiabatic process, $\mathrm{dQ}=0$
$\therefore$ Molar heat capacity $=0$
$\because \mathrm{dQ}=0 \Rightarrow \mathrm{dU}=-\mathrm{dW}$
Also $\mathrm{dU}=\frac{\mathrm{f}}{2} \mathrm{nRdT}$
$\therefore$ Only option (3) is correct.

Asked in: JEE Main 2025 (02 Apr Shift 1)

Practice more Thermodynamics questions on Aicharya