Consider the melting of 1g of ice at `0^(@)C` to was at `0^(@)C` at atmospheric pressure. Then the change in internal energy of the system (density of ice is 920kg/`m^(3)`)?

Options

A. 334J
B. 420J
C. 540J
D. 680J

Answer

A

Explanation

Heat required to change the phase of a solid
`DeltaQ=mL_(f)`
Work done by system at constant pressure,
`DeltaW=P(V_("liquied")-V_("solid"))`
From first law of thermodynamics,
`DeltaU=DeltaQ-DeltaW`
`=mL_(f)-P(V_("liquid")-V_("solid"))`
Latent heat of fusion of water,
`L_(f)=3.335xx10^(5) J//Kg`
`DeltaQ=(1xx10^(-3))(3.335xx10^(5))=334J`
The density of ice is `920 kg//m^(3)`.
`V_("solid")=(1xx10^(-3))/(920)=1.09xx10^(-6)m^(3)`
`V_("liquid")=1xx10^(-6)m^(3)`
`=1.013xx10^(5))(1xx10^(-6)-1.09xx10^(-6))`
`=-9xx10^(-3)J`
Work done by the system is negative because the system is negative because the system decreased in volume.
`DeltaU=DeltaQ-DeltaW=334-(-9xx10^(-3))`
`=334J`