1. A 1.9 kg bar of copper is heated at atmo- spheric pressure of 1.013 × 105 N/m2.If its temperature increases from 28?C to 45?C, find the work done by the copper. The linear expansion coefficient of copper is 1.7 × 10?5 (?C)?1, its density is 8920 kg/m3 and its specific heat is 387 J/kg ·? C.Answer in units of J.2. What quantity of thermal energy is trans- ferred to the copper in this process? The specific heat of copper is 387 J/kg ·? C.Answer in units of J.
The work done by the copper is change in volume multiplied by external pressure. The initial volume of the copper is its mass divided by its density: Vol ( 1.9 kg ) / ( 8920 kg/m? ) 2.13 × 10^4 m? Since ( 1 + x )^3 ≈ 1 + 3x for x 1, the relative change in volume is approximately three times the relative change in length. ?Vol / Vol 3( 1.7 × 10?5 (?C)?1 ) 5.1 × 10^-5 / ?C volumetric expansion coefficient ( VEC ) Work: [ ?Vol ]( pressure ) [ ( Vec )(Vol )( ?T ) ]( pressure ) ( 5.1 × 10^-5 / ?C )( 2.13 × 10^4 m? )( 45?C - 28?C )( 1.013 × 10^5 N/m? ) 0.01871 J ?--- 2. Change in thermal energy is mass × specific heat × change in temperature: ( 1.9 kg )( 387 J / (kg ?C) )( 45?C - 28?C ) 12500 J ?---
