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JIPMER 2015
Exam
JIPMER
Year
2015
Subject
Physics
Chapter
Thermodynamics

JIPMER 2015 · Physics · Thermodynamics

A diatomic gas (γ=1.4) does 200 J of work when it is expanded...

A diatomic gas (γ=1.4)(\gamma=1.4) does 200 J of work when it is expanded isobarically. Find the heat given to the gas in the process.

Options

  1. A500 J
  2. B700 J
  3. C600 J
  4. D900 J

Correct answer

B. 700 J

Step-by-step solution

For a diatomic gas CV=52RC_V=\frac{5}{2} R and Cp=72RC_p=\frac{7}{2} R The work done in an isobaric process is W=p(V2−V1)=nR(T2−T1)⇒T2−T1=WnR\begin{aligned} W & =p\left(V_2-V_1\right)=n R\left(T_2-T_1\right) \\ \Rightarrow T_2-T_1 & =\frac{W}{n R}\end{aligned} The heat given in an isobaric process is Q=nCp(T2−T1)nCpWnR=72W=72×200 J=700 J\begin{aligned} Q & =n C_p\left(T_2-T_1\right) \\ n C_p \frac{W}{n R} & =\frac{7}{2} W \\ & =\frac{7}{2} \times 200 \mathrm{~J} \\ & =700 \mathrm{~J}\end{aligned}
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