- #1
yamata1
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- Homework Statement
- A bottle of water is removed from a cupboard at the initial temperature ##T_i##. In the ambient air of constant temperature ##T_0##, it warms or cools to reach equilibrium at the final temperature
##T_f = T_0##. The heat capacity of the plastic of the bottle is neglected compared to that of the water.
The thermal expansion of the water is also neglected.
a)The heat capacity C of the water depends on the temperature. Express entropy variations
##\Delta S## of water, ##\Delta S_{th}## of the air and ##\Delta S_{univ}## of the universe in the form of integrals.
b) Show that, whatever the temperatures, ##\Delta S_{univ}\geq 0##.
- Relevant Equations
- ##dS=\frac{dQ}{T}##
for a)##\Delta S=\mp \int_{T_i}^{T_0}\frac{C(T)}{T}dT## and ##\Delta S_{th}=\int_{T_i}^{T_0}\frac{dQ}{T_0}dT## so ##S_{univ}=\Delta S_{th}+\Delta S##.
What is ##dQ## equal to ? I don't know how to answer question b).
Thank you for your help.
What is ##dQ## equal to ? I don't know how to answer question b).
Thank you for your help.