Ideal gas Definition and 856 Threads

Hi I built with Python a simulation of an ideal gas in 2D, treating the molecules as hard spheres with elastic collisions. I am trying to test the experimental values of P,T etc. in the simulation versus the theoretical values. however, I have two problems: 1) when comparing the pressure...

Homework Statement Prove that (∂P/∂V) n,T = 1/(∂V/∂P) n,T n and T are supposed to mean that theyre just constants Homework Equations Ideal Gas PV=nRT The Attempt at a Solution I tried (∂P/∂V) n,T= ∂nRT/v/∂V = ∂nRT/V ∂V then I am stuck here

Homework Statement Using the expression for the entropy change of an ideal gas when the volume and temperature change and TV\gamma-1 = constant, show explicitly that the change in entropy is zero for a quasi-static adiabatic expansion from state V1T1 to state V2T2.Homework Equations TV\gamma-1...

Homework Statement An ideal gas is enclosed in a gas syringe. The pressure on the gas is now increased but the temperature of the gas is kept constant. The average kinetic energy of the gas molecules will... A) increase B) remain constant C) decrease D) double Homework Equations...

I'm a third year chemical engineering major and this is my first real thermodynamics class, so I'm not entirely sure what I'm doing. Any help is greatly appreciated! Homework Statement A rigid horizontal cylinder contains a freely moving piston. Initially, it divides the cylinder into equal...

A syringe contains ideal gas. The piston is frictionless and no gas escapes. Once heated slowly, the piston moves outwards. The piston stops moving when the temperature is steady. The pressure of the gas after the piston stops moving remains the same (no change in pressure). What can we say...

In my course they're using the equality U = \frac{p}{\alpha \rho} with alpha some constant (U = internal energy per mass, p = pressure, rho = density). They explicitly derive it for an ideal gas yet later apply it to a liquid (in the context of deriving the Navier-Stokes energy equation). Seems...

what is the reciprocity theorem? and does ideal gas law PV=nRT follows the theorem?

Homework Statement A rigid container holds 2.80 mol of gas at a pressure of 1.20 atm and a temperature of 60.0 degrees Celsius. What is the container's volume? Homework Equations PV=nRT The Attempt at a Solution (2.80*8.31*333)/1.20 = 6457m^3 This answer seems way too big...

Homework Statement A balloon with a constant volume is in 1000C. The fraction of gas flow out of balloon when temperature increased by 20C is nearly equal to (consider pressure and the gas in balloon is ideal) a. 2/373 b. 2/375 c. 2/100 d. 373/375 e. 100/102 Homework Equations...

Could someone please prove why the work done by a gas is the area under a PV diagram? That is, I know that dW=P \text{ }dV, but why is that true physically? I realize that W=f \cdot d \text{ and } F=P \cdot A .Thanks.

Homework Statement 'A closed cylinder containing a perfect gas at 300K is divided into two parts A and B of equal volume, V0 by a freely moveable close-fitting piston. The gas in B is then heated to 400K but that in A is maintained at 300K. Show that the final volume of the gas in B, Vbf =...

Homework Statement The previous part of the question: (a) 1 mole of an ideal gas in a container is at 303,000 Pa, volume is 0.005 m^3. What is the work done by the gas if it expands at constant pressure to twice its original volume? (This was easy enough) The part I'm having trouble...

Homework Statement Argon is stored in a container of volume 2L and a pressure of 5 atmospheres. The amount of gas present is 0.2 moles. Find: (i) The absolute temperature of the gas (ii) The number of atoms of gas in the container (iii) The total mass of the gas (iv) The total internal...

Homework Statement Find the fundamental equation of a monoatomic ideal gas in the Helmholtz potential representation, in the enthalpy representation, and in the Gibbs function representation. Assume the fundamental equation S= \frac{NS_0}{N_0} +NR \ln \left [ \left ( \frac {U}{U_0} \right )...

Homework Statement A buffer at the end of a rail track consists of a hydro-pneumatic shock absorber. The gas chamber of the absorber has an cylindrical geometry consisting of a length of 800mm and 0.5 m diameter and a pressure of 5 bar. Calculate the final pressure and stroke if a 2 tonne...

Homework Statement This is the last part of the question. So far have been made to derive: ## \mu _{\text{JK}}=\left(\frac{\partial T}{\partial P}\right)_H=-\frac{1}{C_P}\left(\frac{\partial H}{\partial P}\right)_T ## Then ##\left(\frac{\partial H}{\partial P}\right)_T=V - T...

Molecules in an ideal gas contained in a vessel are striking the vessels wall. I am trying to find the total kinetic energy of gas molecules striking a unit area of that well per unit time. The number of collisions per unit area per unit time is derived from the normalized Maxwellian...

Homework Statement The closed cylinder of the figure has a tight-fitting but frictionless piston of mass M. the piston is in equilibrium when the left chamber has pressure p0 and length L0 while the spring on the right is compressed by ΔL. a. What is ΔL in terms of p0, L0, A, M, and k...

Homework Statement Assuming that the auxiliary system in the Carnot cycle is a monoatomic ideal gas whose fundamental equation is S=\frac{NS_0}{N_0} +NR \ln \left [ \left ( \frac{U}{U_0} \right ) ^{3/2} \left ( \frac{V}{V_0} \right ) \left ( \frac{N}{N_0} \right ) ^{-5/2} \right ]. 1)Find...

Hi everyone, I'm working through an example in my textbook, and it's making very little sense to me. The problem is: Let Z_1(m) be the partition function for a single quantum particle of mass m in a volume V. First, calculate the partition function for two of these particles if they are...

Homework Statement I'm not able to understand the following equation ΔH = ΔU + (Δn)RT firstly if T is taken to be constant (as the book says), ΔU = 0 if T is not constant then which T i am supposed to put in? initial or final? Homework Equations please help. Thank you. The...

I am a bit confused by the definition of an isentropic process in the flow of an ideal gas. isentropic implies reversible & adiabatic. for a process to be reversible, there are no losses to friction (viscosity in this case), for a process to be adiabatic, there is no heat transfer with...

I'm working through Kardar's Statistical Physics of Particles, and I'm in chapter 4 on the part about the ideal gas. Here's a link to that chapter from the book: http://web.mit.edu/8.333/www/lectures/lec13.pdf I think he has an error in equation IV.33 but I'd like you guys to make sure of it...

Homework Statement A container contains 1g of O_2 at a pressure of 1 atm and temperature T_i=47°C. At a certain time, due to an escape of gas, the pressure is 5/8 atm and the temperature decreases to 27°C. 1)What is the volume of the container? 2)How much mass of O_2 has escaped...

Homework Statement Approximately what fraction of molecules of a gas (assumed ideal) have velocities for which the angle φ lies between 29.5° and 30.5°, while θ lies between 44.5° and 45.5°? Homework Equations The Attempt at a Solution What does the question even mean...

Hi all. I have ran into a problem in converting from imperial to SI units, as follows. The ideal gas constant for air is often given in imperial units as R = 1716 \frac{ft*lbf}{slug*°R} where 1 ft*lbf = 1.356(10^{-3}) kJ 1 slug = 14.59 kg °R = \frac{9}{5}K Thus making these...

Homework Statement the diagram above of pressure P versus volume V shows the expansion of 2.0 moles of a monatomic ideal gas from state A to state B. As shown in the diagram PA = PB = 600 N/m2 , VA = 3.0 m3 and VB = 9.0 m3. a) i) Calculate the work done by the gas as it expands ii)...

I am reading through my thermodynamics book. Going over a air-standard otto cycle example problem. For reference the example problem is as follows: The temperature at the beginning of the compression process of an air-standard Otto cycle with a compression ratio of 8 is 5408R, the pressure...

Homework Statement Find the relation P=P(V) for a transformation dQ=0 in an ideal gas (PV=nRT and U=CnRT).Homework Equations dU=dQ-PdV.The Attempt at a Solution If I assume that C and R are constant I get dU=CR \left [ \frac{\partial (nT)}{\partial n} dn + \frac{\partial (nT)}{\partial T } dT...

Hi, with the ideal gas law we have: cp = CV + (∂V/∂T) * P = CV + Nk (constant P) can someone explain why it intuitively most be so that, the heat capacity at constant pressure is independent of pressure? I mean surely a gas at high pressure wants to expand more?

Oh you who are wise in the ways of Physics, I beg a moment of your time. I've poked around wikipedia and found my way to PV=nRT and Thermal Mass and some other basics, and Googled "compressed air" "ice" "expansion" and similar, but can't quite find anything that helps me answer my question...

μ/T represents the change in entropy if we change the number of particles,, so according to the fundamental assumption of statistical mechanics μ/T should tell us about the tendency of two systems to exchange particles... but I am having a hard time imagining how rotational or vibrational...

I've been working on this problem for a couple of hours, and I can't seem to crack it. I feel like just a tip on how to get started would get me up over the hump. Homework Statement Two pistons in two different cylinders are connected by a rigid rod. A pin used to fix the pistons in place...

I know a gas is ideal if it has a higher T or low P relative to its CP. A probably stated that nitrogen is at 300kPa and 227 deg C. The solutions says its an ideal gas, but how does it know? Is it just same to assume that or is there an actual table that has gas's and their CPs?

Homework Statement What is the pressure inside a $50.0$ L container holding $105.0$ kg of argon gas at $20^\circ$ C?Homework Equations Ideal Gas Law: PV=nRTThe Attempt at a Solution From the ideal gas law, I get P=\frac{nRT}{V}=\frac{\frac{105.0\times 10^3g}{36g/mol}\times 0.08214\frac{L\cdot...

I really need help on this question, I've tried asking several people but I still don't quite get it. The formula for the work done on compressing/expanding an ideal gas is \int-pdV. Now first of all - p denotes the internal pressure of the gas right? If so, good so far. Let us now assume...

I am trying to solve a problem but I am not sure if I am going about it the right way. I am using the ideal gas law to find out the amount of steam it will take to open a relief valve. Using the law I have calculated the amount of steam that will be in a volume but I am not sure if that is also...

Homework Statement You have several identical balloons. You experimentally determine that a balloon will break if its volume exceeds 0.900L . The pressure of the gas inside the balloon equals air pressure (1.00 atm). The air inside the balloon has a constant temperature of 22 C. How many...

Homework Statement A 4.15 mol sample of a diatomic ideal gas (γ = 1.4) expands slowly and adiabatically from a pressure of 5.60 atm and a volume of 13.5 L to a final volume of 34.5 L. Find initial+final temperatures Homework Equations pV/T (all initial) = pV/T (all final) The...

Hi there. I have a silly doubt about the entropy of mixing for ideal gases The entropy of mixing is this (Eq. [1]): S_{mix}=\sum_j N_j s_{j0}+\left (\sum_j N_j c_j \right) R \ln{\frac{T}{T_0}}+\sum_j N_j R \ln {\frac{V}{N_jv_0}} Now I don't know what identity the book uses to rewrite this on...

Ideal Gas Law Problem (Please help!) Show that if the temperature in the atmosphere is independent of altitude, then the pressure as a function of altitude y is p=(p initial)e^(-mgt/kT) Where m is the average mass per molecule of air. I really have no idea where to start. Please help...

can temperature be changed without changing pressure as well as number of molecules for an ideal gas?

Homework Statement A wheel has volume 1.2 x 10-3 m3 when being full. A pump has working volume of 9 x 10-5 m3. How many times do you need to push the pump to fill the air to the wheel (initially there is no air in the wheel) until the pressure is 3.0 x 105 Pa? The atmospheric pressure is 1.0 x...

Homework Statement See attachment "problem". Homework Equations See attachment "data" The Attempt at a Solution Can someone tell me what values to plug in for the equation R/M integral (a+bT+cT^2...). The solution doesn't show this step, so I have no idea the numbers they used to...

Homework Statement A gas mixture of 0.13 mol NH3, 1.27 mol N2, and 0.025 mol H2O vapor is contained at a total pressure of 830 mm Hg and 323 K. Calculate the following: (a) Mole fraction of each component. (b) Partial pressure of each component in mm Hg. (c) Total volume of mixture in m3...

Homework Statement 5 moles of an idea gas at 300K at a pressure of 1.00 x 10^5 Pa is heated to 500K at constant pressure. The amount of heat transferred is 29.1kJ. Determine whether a gas is monatomic or diatomic through consideration of the values of the molar heat capacity at constant...

Homework Statement A gas is in a piston which is at 25 degrees celsius with a volume 4.0L is held in a room at atmospheric pressure. If the temperature is increased to 193 degrees celsius, the piston expands to it's maximum volume. If the pressure in the room is then increased to 4.3 atm, what...

Homework Statement A vacuum pump on Earth can produce a vacuum with a pressure as low as 1.00*10^-8 torr. How many molecules are present in each mL at a temperature of 27.0 degrees Celsius? V = 1mL = 10^-3 L <-- How many sig figs should I use here? Should I make it 1.00*10^-3L or keep it...

I need some help with e), but could someone also check to see if the rest is correct? Homework Statement The velocity component v_x of gas particles in the x-direction is measured and the probability distribution for v_x is found to be P \propto e^{-\frac{-m v_x^2}{2 k_B T}} with m the...