An ideal gas undergoes isothermal compression from 5 m3 to 1 m3 against a constant external pressure of 4 Nm–2. Heat released in this process is used to increase the temperature of 1 mole of Al. If molar heat capacity of Al is 24 J mol–1 K

Engineering

Chemistry

First Law and Various Process

Heat Work and internal Energy

Question

An ideal gas undergoes isothermal compression from 5 m³ to 1 m³ against a constant external pressure of 4 Nm^–2. Heat released in this process is used to increase the temperature of 1 mole of Al. If molar heat capacity of Al is 24 J mol^–1 K^–1, the temperature of Al increases by:

2/3 K

3/2 K

2 K

4 K

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Isothermal ⇒ ΔU=0

so q = – w_irr

= + P_ext. (V₂ – V₁)

= 4 (1 – 5)

= –16 J

For Al

q = n.C_m.ΔT

16 = 1 × 24 × ΔT

$ΔT = \frac{2}{3} K$