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1. A sample of 11.2 g of N2 (nitrogen) gas initially in a volume V1 = 150 mL and T = 500K is expanded isothermally and reversibly to a final pressure p2 = 1.00 atm. Calculate w, q, ?U and ?H. Assume N2 to behave like an ideal gas.

2. The same 11.2 g of N₂ (T = 300K) is expanded now isothermally and irreversibly from V₁ = 150 mL to p₂ = 1 atm, against a constant external pressure p_ext. = 1 atm. Again calculate w, q, ?U and ?H for this irreversible isothermal ideal gas expansion.

3. When 350 J of energy is added as heat to 3.0 mol of a gas kept at constant pressure, the temperature of the gas rises by 2.87 K. Calculate the molar heat capacity, C_m of the gas a) at constant pressure (C_p,m) and b) at constant volume (C_V,m) (assume ideal gas).

4. CaCO₃ in the form of limestone is the starting mineral for the production of cement. In cement kilns, limestone is heated to approximately 1300 K, at which temperature it decomposes to CaO,

64.0 g. of CH4 is heated at constant volume from p1 = 1.00x105 Pa, T1 = 300K until the pressure reaches p2 = 2.00x105 Pa. Again calculate ΔU, ΔH, w and q. CV,m = 24.0 J/K.mol. Assume ideal gas behaviour. question: if constant volume then delta V should be zero so why does the solution manual say w = U-H

Consider a process that occurs at constant volume.

The initial volume of gas is 2.30 L , the initial temperature of the gas is 26.0 °C , and the system is in equilibrium with an external pressure of 1.2 bar (given by the sum of a 1 bar atmospheric pressure and a 0.2 bar pressure due to a brick that rests on top of the piston). The gas is heated slowly until the temperature reaches 51.2 °C . Assume the gas behaves ideally, and its heat capacity at constant volume is: CV,m=14.2J/(K.mol)

Part A

What is the value of w? (J)

Part B

What is the value of q? (J)

Part C

Calculate ΔU

Part D

Calculate Δ H . Remember the definition of enthalpy: H=U+pV, which applied to a process becomes ΔH=ΔU+Δ(pV).

What is thename of Bangladesh  president? 

HOW DO YOU CALCULATE THE joules OF Work

Consider a container with a frictionless piston that contains a given amount of an ideal gas.

Let’s assume that initially the external pressure is 2.20 bar, which is the sum of a 1 bar atmospheric pressure and the pressure created by a very large number of very small pebbles that rest on top of the piston. The initial volume of gas is 0.300 L and the initial temperature is 25°C.

Now, you will increase the volume of the gas by changing the external pressure slowly in a way that guarantees that the temperature of the system remains constant throughout the process. To do this, imagine you remove the pebbles one by one slowly to increase the volume by an infinitesimal amount. Every time you remove a weight you allow the system to equilibrate. Your cylinder is immersed in a water bath at 25°C, which keeps your gas at the same temperature throughout the whole process.

Remember to use three significant figures for all numerical answers. The margin of error for each numerical answer is 1%. To avoid rounding errors use the unrounded intermediate values in your final calculations.

Note: You may find an equation to solve this problem in a textbook or online, but the goal of this challenge is that you think through the problem and come up with the equation on your own. This problem requires basic calculus, so be ready to integrate!

2 with the temperatures T1 < T2 areavailable, and at any given moment of time the heat exchange is established with only one of the reservoirs. In the initial equilibrium state the external pressure is p1 , and heat contact is with reservoir 1. At the same time moment the external pressure is quickly changed to p2 , whereas heat exchange switches to reservoir 2, and we wait for the system to equilibrate. Then the external pressure is quickly returned to its initial value p1 , whereas heat exchange switches back to reservoir 1, and we wait for the system to equilibrate. The system, obviously, returns to its initial state and, therefore we can call our entire process a cycle.

b) (2 pts) For given T1 , T2 , and p1 find the range of values for p2 for which the produced work is positive w > 0 .

Consider n moles of ideal gas kept in a cylinder with a piston. Two heat reservoirs 1 and 2 with the temperatures T1 (reseivor 1) < T2 (reseivor 2) are available, and at any given moment of time the heat exchange is established with only one of the reservoirs. In the initial equilibrium state the external pressure is p1 , and heat contact is with reservoir 1. At the same time the external pressure is quickly changed to p2 , whereas heat exchange switches to reservoir 2, and we wait for the system to equilibrate. Then the external pressure is quickly returned to its initial value p1 , whereas heat exchange switches back to reservoir 1, and we wait for the system to equilibrate. The system, obviously, returns to its initial state and, therefore we can call our entire process a cycle.

a) (10 pts) Calculate the amount of work w the system produce on the environment, the amount of heat q2 , transferred from reservoir 2 (heat source) to the system, and the amount of heat q1 , transferred to reservoir 1 from the system; all for an entire cycle.

b) (2 pts) For given T1 , T2 , and p1 find the range of values for p2 for which the produced work is positive w > 0.

c) (3 pts) In the case w > 0 our process can be considered as a cycle of a heat engine that produces useful work w > 0 , using the amount of heat q2 from the heat source, and dumping the amount of heat q1 to the reservoir (inevitable loss). Find the efficiency η = w/q2 of our heat engine.

d) (5 pts) Based on the first and second laws of thermodynamics find the maximal valueηmax of the efficiency for any heat engine that uses two heat reservoirs at temperatures T1 < T2 . Is our engine more or less efficient? Explain why.

Consider a small system that is interacting with a reservoir at temperature 400 K, pressure 108 Pa, and chemical potential ‒0.3 eV.

(a) To go from state 1 to state 2, the small system must take an additional 0.03 eV of energy and 10‒29 m3 of volume from the reservoir. How many times more probable is it for the small system to be in state 1 than state 2?

(b) To go from state 1 to state 3 the small system must take 0.4 eV of energy and one particle (but no extra volume) from the reservoir. How many times more probable is it that the small system is in state 1 than state 3?

(c) To go from state 1 to state 4, the small system must take no energy but one particle and 10‒27 m3 of volume from the reservoir. How many times more probable is it that the small system is in state 1 than state 4?