Question

1A: How much heat would it take to melt a 9 kg block of ice?

   _________ kJ

1B: How much heat is required to convert 175 g of ice at -4°C to water at 4°C?
   _________ cal

1C: What is the change in length of a metal rod with an original length of 6 m, a coefficient of thermal expansion of 0.00002/°C, and a temperature change of 24°C?
__________ mm

1D: A steel railroad rail is 26.0 m long. How much does it expand during a day when the low temperature is 18°C and the high temperature is 35°C?
________ mm

Answer 1

1A.

Heat required to melt the ice is given by:

Q = m*Lf

Lf = latent heat of fusion = 3.34*10^5 J/kg

Q = 9*3.34*10^5 = 3006000 = 3006 kJ

1B

Heat required will be

Q = Q1 + Q2 + Q3

Q1 = heat required from -4 C ice to 0 C ice = m*Ci*dT1

Q2 = Heat required for melting = m*Lf

Q3 = heat required from 0 C water to 4 C water = m*Cw*dT2

dT1 = 0 - (-4) = 4 C

dT2 = 4 - 0 = 4 C

Ci = Specific heat of ice = 2090 J/kg-C

Cw = 4186 J/kg-C

m = 175 gm = 0.175 kg

So,

Q = m*Ci*dT1 + m*Lf + m*Cw*dT2

Q = 0.175*2090*4 + 0.175*3.34*10^5 + 0.175*4186*4

Q = 62843.2 J

1C.

dL = L0*alpha*dT

dL = 6*0.00002*24

dL = 2.88*10^-3 = 2.88 mm

1D.

dL = L0*alpha*dT

for steel alpha = 11*10^-6 C

dL = 26*11*10^-6*(35 - 18)

dL = 4.86*10^-3 m = 4.86 mm