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WBJEE · Physics · Thermodynamics

\(A\) heating element of resistance \(r\) is fitted inside an adiabatic cylinder which carries a frictionless piston of mass \(m\) and cross section A as shown in diagram. The cylinder contains one mole diatomic current the element temperatures time \(t\) as (a and \(\beta\) are constants), while pressure remains constant. The atmospheric pressure above the piston is \(P_{0}\). Then

  1. A the rate of increase in internal energy is \(\frac{5}{2} R(\alpha+\beta t)\)
  2. B the current flowing in the element is \(\sqrt{\frac{5}{2 r} R(\alpha+\beta t)}\)
  3. C the piston moves upwards with constant acceleration
  4. D the piston moves upwards with constant speed
Verified Solution

Answer & Solution

Correct Answer

(A) the rate of increase in internal energy is \(\frac{5}{2} R(\alpha+\beta t)\)

Step-by-step Solution

Detailed explanation

We know that Internal energy, \(U=\frac{n f R T}{2}=\frac{5 R}{2}\left(\alpha t+\frac{1}{2} \beta t^{2}\right)\) Differentiate with respect to \(t\) \[ \frac{d U}{d t}=\frac{5 R}{2}[\alpha+\beta t] \] But, \(d Q=n C_{p} d T\)…