Crey | The fundamental thermodynamic relation for a rubber band is given by 𝒅𝑼 = 𝑻𝒅𝑺 + 𝝉𝒅𝑳, where 𝑻 is the absolute temperature, 𝑺 is the entropy, 𝝉 is the tension in the rubber band, and 𝑳 is the length of the rubber band. Which one of the following relations is CORRECT: ( ∂ T ∂ S ) L = ( ∂ τ ∂ L ) S , τ = ( ∂ U ∂ S ) L , T = ( ∂ U ∂ S ) τ , ( ∂ T ∂ L ) S = ( ∂ τ ∂ S ) L

Question

The fundamental thermodynamic relation for a rubber band is given by 𝒅𝑼 = 𝑻𝒅𝑺 + 𝝉𝒅𝑳, where 𝑻 is the absolute temperature, 𝑺 is the entropy, 𝝉 is the tension in the rubber band, and 𝑳 is the length of the rubber band. Which one of the following relations is CORRECT:

Options :

${(\frac{\partial T}{\partial S})}_{L} = {(\frac{\partial τ}{\partial L})}_{S}$
$τ = {(\frac{\partial U}{\partial S})}_{L}$
$T = {(\frac{\partial U}{\partial S})}_{τ}$
${(\frac{\partial T}{\partial L})}_{S} = {(\frac{\partial τ}{\partial S})}_{L}$

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