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JIPMER 2010
Exam
JIPMER
Year
2010
Subject
Physics
Chapter
Thermodynamics

JIPMER 2010 · Physics · Thermodynamics

1 mole of an ideal gas at an initial temperature of T ~K does 6 R...

1 mole of an ideal gas at an initial temperature of T KT \mathrm{~K} does 6R6 R joule of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is 5/35 / 3, then final temperature of the gas will be

Options

  1. A(T−4)K(T-4) \mathrm{K}
  2. B(T+4)K(T+4) \mathrm{K}
  3. C(T−2.4)K(T-2.4) \mathrm{K}
  4. D(T+2.4)K(T+2.4) \mathrm{K}

Correct answer

A. (T−4)K(T-4) \mathrm{K}

Step-by-step solution

Work done by gas in adiabatic process, W=nR(Ti−Tf)γ−1∴6R=1×R(T−T2)(53−1) or 6=T−T22/3 or T−T2=4 or T2=(T−4)K\begin{array}{rlrl} & & W & =\frac{n R\left(T_i-T_f\right)}{\gamma-1} \\ \therefore & 6 R & =\frac{1 \times R\left(T-T_2\right)}{\left(\frac{5}{3}-1\right)} \\ & \text{ or } & 6 & =\frac{T-T_2}{2 / 3} \\ & \text{ or } & T & -T_2=4 \text{ or } T_2=(T-4) \mathrm{K} \end{array}
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