Question

The temperature of n moles of an ideal gas changes from T₁ to T₂ in a quasi-static adiabatic transition. Show that the work done by the gas is given by

a) W=nCv(T₂−T₁)
b) W=nCp(T₂−T₁)
c) W=nR(T₂−T₁)
d) W=nRT₁ln(T₂/T₁)
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Answer 1

The work done by an ideal gas in a quasi-static adiabatic transition can be calculated using the formula W = nR(T₂ − T₁).

Step-by-step explanation:

In a quasi-static adiabatic transition for an ideal gas, the work done by the gas can be calculated using the formula: W = nCv(T₂ − T₁), where W is the work done, n represents the number of moles, Cv is the molar specific heat at constant volume, and T₁ and T₂ are the initial and final temperatures, respectively.

To further simplify the equation, we can use the relation Cv = R/(γ - 1), where R is the molar gas constant and γ is the adiabatic index. Substituting this into the formula, we get the alternative equation: W = nR(T₂ − T₁) / (γ - 1).

Hence, the correct option for the work done by the gas is: W = nR(T₂ − T₁) (option c).