JEE Main · 2006 · 30 Apr 2006 · Offline · Heat & Thermodynamics

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The work of 146 kJ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by

7^{\circ} C

. The gas is
(

R = 8.3 J mol^{- 1} K^{- 1}

)

(A)monoatomic
(B)diatomic✓ Correct
(C)triatomic
(D)a mixture of monoatomic and diatomic

Answer: (B)

Solution

In an adiabatic process no heat is exchanged, so the work done in compressing the gas goes wholly into its internal energy:

W = n C_{v} Δ T

. With

n = 1 kmol = 1000 mol

W = 146 kJ

and

Δ T = 7 K

, the molar heat capacity is

C_{v} = \frac{146000}{1000 \times 7} \approx 20.9 J mol^{- 1} K^{- 1}

. This is

\frac{5}{2} R

, the constant-volume molar heat capacity of a diatomic gas, so the gas is diatomic.

JEE Main · 2006 · 30 Apr 2006 · Offline · Single correct option

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