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+2 votes
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in Chemistry by (36.0k points)
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Deduce the mathematical expression of first law of thermodynamics for the following processes :

(1) Isothermal process 

(2) Isobaric process 

(3) Isochoric process 

(4) Adiabatic process.

2 Answers

+4 votes
by (34.5k points)
selected by
 
Best answer

(1) Isothermal process : This is a process which is carried out at constant temperature. Since internal energy, U of the system depends on temperature there is no change in the internal energy U of the system. 

Hence,

ΔU = 0.

By first law of thermodynamics,

ΔU = Q +W 

∴ 0 = Q + W 

∴ Q = -W or W = -Q.

  • Hence in expansion, the heat absorbed by the system is entirely converted into work on the surroundings.
  • In compression, the work done on the system is converted into heat which is transferred to the surroundings by the system, keeping temperature constant.

(2) Isobaric process : In this, throughout the process pressure remains constant. Hence the system performs the work of expansion due to volume change ΔV.

W= -Pext × ΔV

Let QP be the heat absorbed by the system at constant pressure.

By first law of thermodynamics,

ΔU = QP + W.

∴ ΔU = QP – PexΔV 

or QP = ΔU + PexΔV

In this process, the heat absorbed QP is used to increase the internal energy (ΔU) of the system.

(3) Isochoric process : In this process the volume of the system remains constant. 

Hence, 

ΔV = 0. 

Therefore, 

The system does not perform mechanical work.

∴ W = -PΔV = -P × (0) = 0

Let QV be the heat absorbed at constant volume. 

By first law of thermodynamics,

ΔU = Q + W 

∴ ΔU = QV.

(4) Adiabatic process : In this process, the system does not exchange heat, Q with its surroundings.

∴ Q = 0.

Since by first law of thermodynamics, 

ΔU = Q + W 

∴ ΔU = Wad.

Hence, 

(i) the increase in internal energy ΔU is due to the work done on the system by surroundings. This results in increase in energy and temperature of the system.

(ii) if the work is done by the system on surroundings, like expansion, then there is a decrease in internal energy (-ΔU) and temperature of the system decreases.

+1 vote
by (17.0k points)

Mathematical expression of 1st law of thermodynamics for-

(1) Isothermal process:

Δu = q + W

∴ Δu = 0

W = −q

(2) Isobaric process:

Δu = q + W

Δu = qp - pexΔv

(3) Isochoric process:

Δu = q + W

∴ W = −pexΔv

Δu = q − pexΔv

(4) Adiabatic process:

Δu = q + W 

∴ q = 0

Δu = W

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