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MHT CET · Physics · Thermodynamics

One mole of an ideal gas at an initial temperature of ' \(T\) ' K does ' 6 R ' of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is \(5 / 3\), the final temperature of gas will be (\(\left.\mathrm{R}=8.31 \mathrm{~J} \mathrm{~mole}^{-1} \mathrm{~K}^{-1}\right)\)

  1. A \((T+4 \cdot 2) K\)
  2. B \((\mathrm{T}-4 \cdot 2) \mathrm{K}\)
  3. C \(\quad(T+4) K\)
  4. D \((T-4) K\)
Verified Solution

Answer & Solution

Correct Answer

(D) \((T-4) K\)

Step-by-step Solution

Detailed explanation

For an adiabatic process,
\(\mathrm{W}=\frac{\mathrm{nR}\left(\mathrm{~T}_{\mathrm{i}}-\mathrm{T}_{\mathrm{f}}\right)}{\gamma-1}\)
\(\begin{array}{ll}\therefore \quad & 6 R=\frac{R\left(T-T_f\right)}{\left(\frac{5}{3}-1\right)} \quad \ldots .\text{(Given: } \mathrm{n}=1) \\ \therefore & T_f=(T-4) K\end{array}\)