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Identification of Different Process

Two moles of ...

Question

Two moles of a perfect gas undergo the following processes
(i) a reversible isobaric expansion from (1.0 am, 20.0L) to (1.0 atm, 40.0 L)
(ii) a reversible isochoric change of state from (1.0 atm, 40.0 L) to (0.5 atm, 40.0 L);
(iii) a reversible isothermal compression from (0.5 am, 40.0 L) to (1.0 atm, 20.0 L)
What is the total heat exchange here in Joules?

$l n 2 = 0.7, l n 3 = 1.1, R = 1 / 12 L a t m / m o l, 25 / 3 J / m o l K, 1 L a t m = 101 J$

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Solution

Cyclic process:
For cyclic process change in state function must be zero thus
$Δ E = 0$ for this cyclic process
$Δ E = Q + W$
$Q = - W = w_{i} + w_{i i} + w_{i i i} (1)$
work done in isobaric process
$w_{i} = - P Δ V = - 1 \times (40 - 20) = - 20 L a t m$
work done in isochoric process and we know that for isochoric process $d v = 0$
$w_{i i} = - p d v = 0$
work done in isothermal process:
$p v = n R T = 0.5 \times 40 o r 1 \times 20 = 20 L a t m$
$w = - n R T l n \frac{v_{i n t i a l}}{v_{f i n a l}}$

$w_{i i i} = - 20 \times l n \frac{40}{20}$ $L a t m$
on substituting in (1) we get
$Q = 606 J$

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Similar questions

Q. Two moles of a perfect gas undergo the following processes
(i) a reversible isobaric expansion from (1.0 am, 20.0L) to (1.0 atm, 40.0 L)
(ii) a reversible isochoric change of state from (1.0 atm, 40.0 L) to (0.5 atm, 40.0 L);
(iii) a reversible isothermal compression from (0.5 am, 40.0 L) to (1.0 atm, 20.0 L)
What is the total heat exchange here in Joules?

l n 2 = 0.7, l n 3 = 1.1, R = 1 / 12 L a t m / m o l, 25 / 3 J / m o l K, 1 L a t m = 101 J

Q. Two moles of a perfect gas undergo the following processes
I. A reversible isobaric expansion from (1.0 atm. 20 L) to (1.0 atm, 40 L)
II. A reversible isochoric exansion from (1.0 atm, 40 L) to (0.5 atm, 40 L)
III. A reversible isothermal compression from (0.5 atm, 40 L) to (1.0 atm. 20 L)
Calculate the total work done (W) involved in the above processes.

Q. Two moles of a perfect gas undergo the following process:

(a) A reversible isobaric expansion from (

1

20 L

1

40 L

)

(b) A reversible isochoric change of state from (

1

40 L

0.5

40 L

)

(c) A reversible isothermal compression from (

0.5

40 L

1

20 L

)

(i) Sketch with labels each of the process on the same P-V diagram.

(ii) Calculate the total work

(w)

and the total change

(q)

involved in the above process

(iii) What will be the value of

Δ U, Δ H, Δ S

for the overall process?

Q. A sample of one mole of an ideal gas at 1.0 atm and 300 K.

(C_{p} = 7 / 2 R)

is put through the following:

a) Constant volume heating to twice its initial temperature
b) Reversible adiabatic expansion back to its initial temperature
c) Reversible isothermal compression to 1.0 atm.
(take

l n 2 = 0.3, R = \frac{25}{3}

in SI units)

Match the following:

\begin{matrix} Quantity & Value P & w_{b} & I & 0 k J Q & w_{c} & I I & - 6.25 k J R & q_{t o t} & I I I & 4.375 k J S & Δ E_{t o t} & I V & 1.875 k J \end{matrix}

Q. An ideal gas undergoes a reversible isothermal expansion from state

I

I I

followed by a reversible adiabatic expansion from state

I I

I I I

The correct plot(s) representing the changes from state

I

I I I

(p : pressure, V : volume, T : temperature, H : enthalpy, S : entropy)

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