Find heat given to gas to take it from A to B. (Given: $C_v = 21$ S.I. units, $P_2 = 30$ Pa, $P_1 = 21.7$ Pa, $R = 8.3$ S.I. units, $n = 10$ moles)

Question

For reaction $A \rightleftharpoons B$, $\Delta G^{\circ} = 105 - 35 \log T$. Find the transition temperature (in $^{\circ} C$) of the above reaction at 1 bar.

Answer 1

Step 1: Identify the nature of work done

From the P–V diagram, the process A → B occurs at constant volume.

Hence, work done during the process is zero.

W = 0

Step 2: Apply first law of thermodynamics

According to the first law:

Q = ΔU + W

Since W = 0 for an isochoric process:

Q = ΔU

Step 3: Expression for change in internal energy

For an ideal gas, change in internal energy is given by:

ΔU = (C_v / R) × (P₂ − P₁)V

Step 4: Substitute given values

C_v / R = 21 / 8.3
P₂ − P₁ = 30 − 21.7

Q = (21 / 8.3) × (30 − 21.7)

Step 5: Final calculation

Q = 21 J

Final Answer:

The heat supplied to the gas during the process is
Q = 21 J

Find heat given to gas to take it from A to B. (Given: $C_v = 21$ S.I. units, $P_2 = 30$ Pa, $P_1 = 21.7$ Pa, $R = 8.3$ S.I. units, $n = 10$ moles)

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The Correct Option is B

Solution and Explanation

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