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n moles of an ideal gas undergoes a process A → B as shown in the diagram. The maximum temperature of the gas during the process is

Options

  1. A3 P 0 V 0 2 nR
  2. B9 P 0 V 0 4 nR
  3. C9 P 0 V 0 2 nR
  4. D9 P 0 V 0 nR

Correct answer

B. 9 P 0 V 0 4 nR

Step-by-step solution

Since the P-V graph of the process is a straight line and two points (V 0 , 2P 0 ) and (2V 0 , P 0 ) are known, its equation will be P - P 0 = 2 P 0 - P 0 V 0 - 2 V 0 V - 2 V 0 = P 0 V 0 2 V 0 - V ∴ P = 3 P 0 - P 0 V V 0 According to the equation for an ideal gas, T = pV nR = 3 P 0 - P 0 V V 0 V nR = 3 P 0 V 0 V - P 0 V 2 nR V 0 ...(i) For T to maximum, dT dV = 0 3 P 0 V 0 - 2 P 0 V = 0 or V = 3 V 0 2 ...(ii) Putting this value in Eq. (i), we get T max = 3 P 0 V 0 3 V 0 2 - P 0 9 4 V 0 2 nR V 0 = 9 P 0 V 0 4 nR

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