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Question:

An ideal gas undergoes isothermal compression from 5m³ to 1m³ against a constant external pressure of 4 Nm⁻¹. Heat released in this process is used to increase the temperature of 1 mole of Al. If molar heat capacity of Al is 24 Jmol⁻¹K⁻¹, the temperature of Al increased by:

23K

32K

1K

2K

Solution:

Work Done on isothermal irreversible for ideal gas W = −Pext(V₂−V₁) = −Pext × ΔV = 4N.m⁻¹ × (1−5)m³ = 4N.m⁻¹ × −4m³ = −16N.m
For Isothermal process , ΔU = 0
q = −W = 16J
Heat used to increase temperature q = nCmΔT
n = 1; Cm = 24J/(mol.K)
Substituting the Values , we get
ΔT = 16J/(1mol × 24Jmol⁻¹K⁻¹) = 2/3 K ≈ 0.67 K
However, there seems to be a mistake in the calculation or the given options. The correct answer based on the provided data is approximately 0.67 K. None of the provided options match this result.