Question

If the mass of a Boeing 747 is 183,025 kg and a space shuttle is 2,030,000 kg, use the specific

heats to explain why aluminum or aluminum composites are the preferred metal for building

these machines if the temperatures they are subjected to range from -54 °C to 150 °C for planes

and -121°C to 1649°C for space shuttles. The specific heats of Fe is 449 J/kg*K, Ti is 523 J/kg*K,

Al is 897 J/kg*K, and carbon fiber composites are 2020 J/kg*K. Why aren’t carbon fiber

composites preferred?

Answer 1

Specific heat is the heat energy required to raise the temperature of the body by 1 deg K per kg mass. When the body is cooled equal amount of heat is given out by the object.

Boeing mass = 183025 kg

temp range = -54 C - 150 C = 200C

heat exchange over the temp. range

Q = 200 * 183025 C_s ; C_s is the specific heat

with iron Q = 200*183025*449 = 16435645000‬ J

with Ti = 200*183025* 523 = 19,144,415,000 J

with Al = 200*183025* 897 = 32,834,685,000 J

with Carbon fiber = 200*183025* 2020 =  73,942,100,000 J

Carbon fiber has the maximum heat exchange compared to other materials over the temperature range.

The heat absorbed by the body will be transferred to the interior or if the outside temp are lower then internally we need generate more heat to compensate the heat loss. It is preferable to have a material with less heat exchange.

n the lower temp. range for the material with higher specific heat, It takes longer time for the material to come in equilibrium with the surrounding and the heat loss from the interior is less.

The lower limit of temp . is around -50 C and the upper limit is 150 in case of Boeing and 1700 C in case of space shuttle. Higher temp. range is much larger than the lower range.

Aluminium is optimum in the lower and higher temperature ranges.

Iron and Ti have lesser specific heat compared to Aluminium. But their densities are higher . If we these material weight of the body increases and the heat quantity also increases. Apart from heat consideration, increasing weight require more thrust power to lift the body. Other material properties like elasticity, brittleness also play an important role for consideration.