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A given ideal gas with = C_p C_v =1.5 at a temperature T . If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be

Options

  1. A2 2 T
  2. B4 T
  3. C2 T
  4. D8 T

Correct answer

C. 2 T

Step-by-step solution

T V^ -1 = constant aligned & T₁ V₁^ -1 = T ₂ V₂^ -1 & T(V)^ 1 / 2 = T ₂ ( V 4 )^ 1 / 2 & [ =1.5, T₁=T, V₁=V and V₂= V 4 ] & T₂= ( 4 V V )^ 1 / 2 T=2 T aligned

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