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The ideal gas equation you try to use for understanding does not provide a full description. To completely describe a thermodynamical system, you need the relevant thermodynamic potential, which here is the internal energy if I understood well your formulation (is a bit vague). Processes like the isobaric expansion occuring here, cannot be explained through ...


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You are correct. In a real process, one would modify this formula to include the so-called polytropic exponent $n$ such that $PV^n=const$. This reflect that the process is not perfectly isentropic. For a fixed final volume this means the final temperature and pressure will be higher than in the ideal case, and more work need to be expended.


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The idea of the question is to find the temperature at which the average interparticle spacing is equal to the average de Broglie wavelength. Both of these are averages because the atoms of the ideal gas are not evenly spaced and the velocity (and therefore de Broglie wavelength) of the ideal gas atoms follows the Maxwell-Boltzmann distribution. So this is ...


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"The size of a single gas particle" is a bad term for what you calculate. A better term would be: "The volume one of the gas particles would occupy, if the total volume were distributed equally among all gas particles" And this translates loosely to "The volume, in which you find one gas particle on average" If you then imagine every particle sitting at ...


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Why would the temperature of the gas in the balloon be fixed? Note that it will depend, among other things, on the thermal conductivity of the rubber of the balloon: if the thermal conductivity were zero, the gas in the balloon would expand isentropically, rather than isothermally.


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Mass conservation assuming stationary conditions: $$\rho(x,t)v(x,t)=\rho(0,t)v(0,t):=\rho_0(t)v_0(t),$$ or equivalently $\rho(x,t)q(x,t)=\rho_0(t)q_0(t)$ since $q=vA$, with $A$ a constant cross section. Therefore $$q(x,t)=\frac{\rho_0(t)q_0(t)}{\rho(x,t)}.$$ Then, we use the initial conditions $$q_0(t)=-\frac{V}{\rho_0(t)}\frac{d \rho_0(t)}{dt},$$ and you ...


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Effectively ideal gases are pretty easy to come by. Air at SATP would be a good example. To be a little more precise, what you're looking for is that the mean free path $\lambda \gg \sigma$, the diameter of the molecules. Basically this just means that molecules spend most of their time far away from each other. You can find $\lambda$ by: ...


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Almost there. Since this looks like a homework question I'll just give a hint. The force balance equation is due to the buoyancy force which is due to the difference in density inside the ballon vs. outside the ballon. Once you work that out, the weight that you missing will come back into the equation.


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The air inside the balloon is less dense than the air outside; this difference is what causes the lift for the balloon. When you heat the air in the balloon, it expands until the balloon is full. At this point the balloon is still on the ground since there is not enough lift. You need to heat the air more, which expands the air more and causes some of the ...


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Start with an ideal gas, $$ V=\frac{nRT}p $$ Then take the natural logarithm of this: $$ \ln V=\ln T+\ln\frac{nR}{p} $$ The derivative of both sides with respect to $T$ gives $$ \frac{d\ln V}{dT}=\frac{d\ln T}{dT}+\frac{d\ln\frac{nR}{p}}{dT}=\frac{d\ln T}{dT}=\frac{1}{T} $$ where we assume an isobaric situation so that $p$ contributes nothing. The left hand ...


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Thermodynamics has simple answers to offer regarding reversibility or otherwise of a given process. For a process to be reversible, it must be reversible at every point along the path ie, the system must be in equilibrium, both internally having well defined values for its properties such as temperature, pressure , internal energy etc., and externally with ...


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In hydrodynamics, conservation means that what flows into the control volume is equivalent to the flow out of the control volume. With respect to momentum, we mean precisely that any change in momentum of the fluid within a control volume is due to the net flow of fluid into the volume and the action of external forces on the fluid within the volume ...


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Once you have the two laws for isothermic and isochoric processes for a perfect gas, you can deduce the state equation. We assume that there exists a “set of possible configurations $(P,V,T)$”, where the two laws (isothermal, isochoric) are both satisfied: $$PV=\phi (T),\quad T=P\xi (V),$$ for some functions $\phi,\xi$. We can then show that $\phi$ is the ...


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According to Boyle's law: At constant temperature a volume gas is inversely proportionally to applied pressure this is boyle's law.


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To my knowledge, there isn't a specific term for these types of gasses. In your question you name "substance" while you list elements. Many different molecules are gaseous at room temperature; however, only a few of the elements are. I'll look at both. They come from different parts of the periodic table but do have a couple of features in common: ...


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The volume of a fixed mass of gas is inversely proportional to its pressure at constant temperature . This is known as Boyle's law. P1 V1=P2 V2 PV =a constant P inversely proportional to 1/V at constant T. PV = a constant T. This is mathematical equation or algebraic law for Boyele's law.



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