How much work must be done by an external agent to raise the temperature of one

Question

How much work must be done by an external agent to raise the temperature of one mole of an ideal diatomic gas by 100 K at constant pressure? A. 250 R B. 100 R C. 350 R D. 150 R E. We need to know the pressure to answer this question The figure shows a closed cycle for a gas (the figure is not drawn to scale). The change in the thermal energy of the gas as it moves from a to c along the path abc is -215 J. As it moves from c to d, 185 J must be transferred to it as heat. An additional transfer of 70 J as heat is needed as it moves from d to a. How much work is done on the gas as it moves from c to d? A. 40J B. 0J C. -40J D. 100J E. -100J

Explanation / Answer

10. one mole ideal diatomic gas
   n = 1
   degree of freedon, f = 5
   tgamma = 1 + 2/f = 7/5
   Cp - Cv = R
   Cp/Cv = gamma
   Cv(gamma - 1) = R
   Cv = R/(gamma -1)
   Cp = gamma*R/(gamma - 1)

   at constant pressure
   Cp = 7R/2
   n = 1
   dT = 100 K
   so heat input, Q = nCp dT = 1*7R/2 * 100 = 2908.5 J = 350 R

   so the external agent has to input 350 R of work

option C.

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