Question

Cp of a gas is 20 J mol\(^{-1}\) K\(^{-1}\). If one mole of the gas is cooled from 298 K to 258 K at constant pressure, calculate the internal energy change of the system. (R = 8.3 J mol\(^{-1}\) K\(^{-1}\))

• A. 468 J
• B. 1.215 kJ
• C. 345 J
• D. 587 J

Hint:

Use relation \(C_p - C_v = R\) to switch between heat capacities in thermodynamics problems.

Answer 1

The Correct Option is A

Step 1: Relating ΔU to temperature change.
ΔU = n C_v ΔT, where C_v = C_p - R.

Step 2: Computing C_v.
C_v = 20 - 8.3 = 11.7 J mol⁻¹ K⁻¹.

Step 3: Temperature drop.
ΔT = 258 - 298 = -40 K.

Step 4: Calculating ΔU.
ΔU = 1 × 11.7 × (-40) = -468 J.

Step 5: Interpreting the sign.
The negative value denotes a decrease in internal energy; magnitude is 468 J.

Step 6: Conclusion.
The change in internal energy is 468 J.