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This question has a lot of flaws to be a college chemistry question. Therefore, I decided to give some insight even though this is a clearly a homework question. The question did not have enough data such as the ebullioscopic constant ($K_b$) of benzene and the van't Hoff factor ($i$) of the solute. At least you can find the ebullioscopic constant of ...


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For completeness, since there is already a well-explained answer addressing how and why $\mathrm{d}U=0$ for an isothermal process is a hallmark of an ideal gas, here is a short derivation of a general expression for the energy. Start from the total differential for the free energy: $$ \mathrm{d}U = \left(\frac{\partial U}{\partial V}\right)_T \mathrm{d}...


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As we know, $$\Delta U=nC_V\,\Delta T$$ And in isothermal process $\Delta T=0$ $$\Rightarrow\Delta U=0$$


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I was told, $\mathrm{d}U=0$ in isothermal process. That is not generally true. It is, however, true for ideal gases, which is probably what you were discussing. No attractive or repulsive forces exist between ideal gas particles. Hence the only type of internal energy an ideal gas can have is kinetic energy, i.e., energy due to the motion of its ...


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The internal energy of an ideal gas is simply $$ U = \alpha nRT,$$ where $$\alpha = \frac{\text{degrees of freedom}}{2}$$ So, in an isothermal process, $$\begin{align} \Delta T &= 0 & \Longrightarrow & &\Delta U &= \alpha nR\Delta T = 0, \end{align}$$ and likewise any $$\left(\frac{\partial U}{\partial P}\right)_T = \left(\frac{\partial U}...


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The atomic/molecular/formula weight (choose whichever is appropriate) of a substance is an intensive property (it is inherent to the substance itself, and is independent of how much of the substance you have), and is independent of temperature (if you raise the temperature high enough to cause a chemical or nuclear reaction, it's no longer that substance). ...


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After looking at the list in the Wikipedia article linked in the comment by M.Farooq, I suspect there are few properties that are guaranteed to be independent of temperature, an exception being molality and mole fraction in a closed system and absence of reactions. Other concentrations that are functions of volume are bound to be functions of temperature. ...


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The given phase diagram provides some information on the time-temperature relationship for the formation of pearlite (P), bainite (B), and martensite (M) from austenite (A) form, which is known as known as gamma-phase iron ($\gamma$-$\ce{Fe}$). For example, It would take $\pu{10 sec}$ to 100% austenite to the 50% austenite-to-pearlite transformation to ...


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