Question

A spring-loaded piston-cylinder contains 1 kg of carbon dioxide. This system is heated from 104 kPa and 25 °C to 1,068 kPa and 311 °C. Determine the total heat transfer to this system in kJ. Give your answer with three decimal points

Answer 1

Q = -68.859 kJ

Step-by-step explanation:

given details

mass
`co_2 = 1 kg`

initial pressure P_1 = 104 kPa

Temperature T_1 = 25 Degree C = 25+ 273 K = 298 K

final pressure P_2 = 1068 kPa

Temperature T_2 = 311 Degree C = 311+ 273 K = 584 K

we know that

molecular mass of
`co_2 = 44`

R = 8.314/44 = 0.189 kJ/kg K

c_v = 0.657 kJ/kgK

from ideal gas equation

PV =mRT

`V_1 = (m RT_1)/(P_1)`

`=(1*0.189*298)/(104)`

`V_1 = 0.5415 m3`

`V_2 = (m RT_2)/(P_2)`

`=(1*0.189*584)/(1068)`

`V_1 = 0.1033 m3`

WORK DONE

`W =P_(avg)*{V_2-V_1}`

w = 586*(0.1033 -0.514)

W =256.76 kJ

INTERNAL ENERGY IS

`\Delta U  = m *c_v*{V_2-V_1}`

`\Delta U  = 1*0.657*(584-298)`

`\Delta U  =187.902 kJ`

HEAT TRANSFER

`Q = \Delta U  +W`

= 187.902 +(-256.46)

Q = -68.859 kJ