An ideal gas undergoes isothermal compression from 5 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 :

Question

An ideal gas undergoes isothermal compression from 5 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 : (A) (3/2) K (B) (2/3) K (C) 1 K (D) 2 K

Tardigrade Admin · Accepted Answer

Work done on isothermal irreversible for ideal gas

= - P_{e x t} (V_{2} - V_{1})

= - 4 N / m^{2} (1 m^{\frac{1}{3}} - 5 m^{3})

= 16 N m

Isothermal process for ideal gas

Δ U = 0

q = - w

= - 16 N m

= - 16 J

Heat used to increase temperature of

A ℓ

q = n C_{m} Δ T

16 J = 1 \times 24 \frac{J}{mol . K} \times Δ T

Δ T = \frac{2}{3} K

$\frac{3}{2} K$

$\frac{2}{3} K$

$1 K$

$2 K$

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

23​K

32​K

1K

2K

Work done on isothermal irreversible for ideal gas =−Pext​(V2​−V1​) =−4N/m2(1m31​−5m3) =16Nm Isothermal process for ideal gas ΔU=0 q=−w =−16Nm =−16J Heat used to increase temperature of Aℓ q=nCm​ΔT 16J=1×24mol.KJ​×ΔT ΔT=32​K

$\frac{3}{2} K$

$\frac{2}{3} K$

$1 K$

$2 K$