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(Solved): ( 20 points) (Variable Specific Heat of Air): As shown in class, the specific heat of air is not c ...



( 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 0.6821

where T is in K and

c_(v )

is in

k(J)/(k)g^(**)K

. Suppose

0.1kg

of air is contained in a rigid vessel at atmospheric conditions of

300K

and

100kPa

. Then,

1200W

of 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 )?



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