JEE MAIN - Chemistry (2019 - 10th January Evening Slot - No. 14)
An ideal gas undergoes isothermal compression from 5m3 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 :
$${2 \over 3}K$$
$${3 \over 2}K$$
1 K
2 K
Explanation
Work done on isothermal irreversible for ideal gas
= $$-$$Pext (V2 $$-$$ V1)
= $$-$$4 N/m2 (1 m3 $$-$$ 5m3)
= 16 Nm
Isothermal process for ideal gas
$$\Delta $$U = 0
q = $$-$$ w
= $$-$$ 16 Nm
= $$-$$ 16 J
Heat used to increase temperature of Al
q = n Cm $$\Delta $$T
16 J = 1 $$ \times $$ 24 $${J \over {mol.K}}$$ $$ \times $$ $$\Delta $$T
$$\Delta $$T = $${2 \over 3}$$K
= $$-$$Pext (V2 $$-$$ V1)
= $$-$$4 N/m2 (1 m3 $$-$$ 5m3)
= 16 Nm
Isothermal process for ideal gas
$$\Delta $$U = 0
q = $$-$$ w
= $$-$$ 16 Nm
= $$-$$ 16 J
Heat used to increase temperature of Al
q = n Cm $$\Delta $$T
16 J = 1 $$ \times $$ 24 $${J \over {mol.K}}$$ $$ \times $$ $$\Delta $$T
$$\Delta $$T = $${2 \over 3}$$K
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