( 20 points) (Variable Specific Heat of Air): As shown in class, the specific heat of air is not completely constant with temperature. As a first approximation, the constant volume specific heat can be given by:
c_(v)(T)=0.0001T 0.6821where T is in K and
c_(v )is in
k(J)/(k)g^(**)K. Suppose
0.1kgof air is contained in a rigid vessel at atmospheric conditions of
300Kand
100kPa. Then,
1200Wof heat is added to the air until its temperature reaches 800 K . Heat losses to the environment can be neglected. (a) ( 3 points) Determine the volume of the vessel. (b) ( 12 points) Determine the time that this process will take. You will need to set up a transient energy balance equation and then perform an integration. HINT: Be careful with units when calculating. (c) ( 5 points) How would your answer to part (b) compare if you used a constant volume specific heat at the averaged temperature during the process (i.e. 550 K )?