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
1. \(\frac{3}{2}K\)
2. 1K
3. 2K
4. \(\frac{2}{3}K\)

Answer 1

Correct Answer - Option 4 : \(\frac{2}{3}K\)

Concept:

It is an irreversible isothermal compression of an ideal gas. 

(i) dE = dq + p(V_f – V_i)

where, dE = Internal energy change

where, dq = amount of heat released

⇒ 0 = dq + p(V_f – V_i)

[∵ dE = 0 for an isothermal process]

⇒ dq = -4(1 – 5) = 16 J

(ii) dq = n × C × ∆T (for Al)

⇒ 16 J = 1 mol × 24 J mol^-1 K^-1 × ΔT

\(\Rightarrow \Delta T = \frac{{16}}{{24}}{\rm{K}} = \frac{2}{3}{\rm{K}}\)