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A square steel bar of side length w = 0.13 m has a thermal conductivity of k = 14 J/(s?m?ÂC) and is L = 2.8 m long. Once end is placed under a candle so that the temperature is T1 = 75Â C while the other end rests on a block of ice so that the temperature is a constant T2. 1) Input an expression for the heat transferred to the cold end of the bar as a function of time, using A = w2 as the cross-sectional area of the bar. 2) How much energy, in joules, was conducted in 1 hour, assuming T2 = 0Â C? 3) Input an expression for the mass of the water melted in 1 hour using Q1 from above and Lf the latent heat of fusion.

Sagot :

The amount of energy required for heat transfer and mass of melted ice  is 25917.84J and 77.83g respectively.

  1. Latent heat arises from the work required to overcome the forces that hold the atoms or molecules within the material together. The regular structure of crystalline solids is maintained by the attractive forces between individual atoms. The attractive force oscillates slightly around its mean position in the crystal lattice.
  2. As the temperature increases, these movements become more violent, and at the melting point the attractive forces are no longer sufficient to maintain the stability of the crystal lattice. However, additional heat (latent heat of fusion) must be supplied (at constant temperature) to make the transition to a more disordered liquid state. In the liquid state, individual particles are no longer held at fixed grid points. It can move freely in liquids.
  3. Liquids differ from gases in that the attractive forces between particles are sufficient to maintain long-range order, which gives liquids some degree of cohesion.
  • The heat conduction formula is,

kA(T1-T₂)/L=Q

Q(t) =Q

Q(t) is the heat transfer as function of the time.

  • The heat transfer as function of the time is,

kw²(T₁-T₂)t

=(14J/sm°C)(0.13m)2(75°C-0°C)(1h 36008

2.8m

= 25917.84J

  • The amount of heat energy needed to to melt the ice is,

Q = mL

Therefore, m =Q/L

=2.5917*10 J / 3.33*105J/kg

= .07783 kg = 77.83g

So, 77.83g of amount ice will be melt

To study about Latent heat-

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