Question
A heat engine carries one mole of an ideal mono-atomic gas around the cycle as shown in the figure. Select the correctoption :
A heat engine carries one mole of an ideal mono-atomic gas around the cycle as shown in the figure. Select the correctoption :
A.
$${q_{AB}} = 450\,R\,\,{\text{and}}\,\,{q_{CA}} = - 450\,R$$
B.
$${q_{AB}} = 450\,R\,\,{\text{and}}\,\,{q_{CA}} = - 225\,R$$
C.
$${q_{AB}} = 450\,R\,\,{\text{and}}\,\,{q_{CA}} = - 375\,R$$
D.
$${q_{AB}} = 375\,R\,\,{\text{and}}\,\,{q_{CA}} = - 450\,R\,$$
Answer :
$${q_{AB}} = 450\,R\,\,{\text{and}}\,\,{q_{CA}} = - 375\,R$$
Solution :
For monoatomic gas $${C_v} = \frac{3}{2}\,R\,{C_p} = \frac{5}{2}\,R$$
At constant volume, $$\Delta U = {q_v} = n{C_{v,m}}\,\Delta T$$
At constant pressure, $$\Delta H = {q_p} = n{C_{p,m}}\,\Delta T$$
For monoatomic gas $${C_v} = \frac{3}{2}\,R\,{C_p} = \frac{5}{2}\,R$$
At constant volume, $$\Delta U = {q_v} = n{C_{v,m}}\,\Delta T$$
At constant pressure, $$\Delta H = {q_p} = n{C_{p,m}}\,\Delta T$$