One mole of oxygen gas is made to undergo a process in which its molar heat capacity C depends on its absolute temperature T as C = α T , where α is a positive constant. Work done by the gas when heated from an initial temperature T 0 to a final temperature 2 T 0 will be

Question

One mole of oxygen gas is made to undergo a process in which its molar heat capacity C depends on its absolute temperature T as C = α T , where α is a positive constant. Work done by the gas when heated from an initial temperature T 0 to a final temperature 2 T 0 will be, 4 α T 0 2, α T 0 - R 3 T 0 2, 3 α T 0 - 5 R T 0 2, none of these

MARKS App · Accepted Answer

C = C v + W ' ⇒ W ' = d W n d T (where W ' is the work done by the gas per unit mole per unit rise in temperature) ⇒ W ' = α T - C v = α T - 5 R / 2 Δ W = ∫ W ' d T = ∫ T 0 2 T 0 α T - 5 R 2 d T = 3 α T 0 - 5 R T 0 2

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