- #1

timetraveller123

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## Homework Statement

2.00 moles of gas is held in a cylinder with a piston and is initially held at 0.300atm and has an initial volume of 0.200 m^3. The molar heat capacity of the gas at constant volume is 24.94 J mol^−1 K^−1

. The gas is then brought from this initial state (State A) through the following processes:

From state A to B:

Gas is allowed to expand isothermally.

From state B to C:

The temperature of the gas drops by 100 K while it is being held at constant volume.

From state C to A:

The volume of the gas is then compressed in an adiabatic process back to its initial state.

(a) What is the initial temperature of the gas in state A?

(b) What is the ratio of the molar heat capacity at constant pressure (C P to the molar heat capacity at constant volume (C V ) of the gas?

(c) What is the volume of the gas at state C? Hence, sketch a P −V

curve depicting the processes, indicating the pressure and volume at each point.

(d) In which of the processes is heat being transferred to the system and in which process is the heat being expelled from the system? Hence, calculate the network done by the system.

(e) Assume that process B to C is instead stated as “The temperature of the gas rises by 100 K while it is being held at constant volume.” Is it possible then to return the gas to its initial state via an adiabatic process? Why or why not

## Homework Equations

q = n cv ΔT

Δu = Q - w

p v^ϒ = constant for adiabatic process

pv = nrt

cp = r + cv

## The Attempt at a Solution

i solved part a and b but got stuck at c i have shown my answer for a and b

a)T = pv/nr = 364K

b)cp /cv = 1+ r/cv = 1.33

c)so for c how am i supposed to know the volume at c without knowing the pressure at c please help thanks!