Question

Saturated steam at 100.0°C is heated to 350.0°C.

What is the required heat input (J/s) if a continuous stream flowing at 100 kg/s undergoes the heating process at constant pressure?

What is the required heat input (J) if 100 kg undergoes the heating process in a constant-volume container?

Use Steam Tables.

Answer 1

When the temperature increases at constant volume,internal energy of the system increases

The relationship between increase in temperature and increase in internal energy is

U_v = C_vT_v

where Cv is heat capacity

At constant volume change in internal energy can be identified with heat supplied at constant temperature

U_v = q T_v

q =U_v /T_v

Here,

100kg saturated H₂O(vapour) at 100^oC----->[system]----->100kg saturated(vapour) H₂O at 350^oC

1)

Heating process occurs at constant pressure

so, q =U_v /T_v

we need to find internal energy at 100^oC and 350^oC

Internal energy of saturated steam at 100^oC is 2506 KJ/Kg

Internal energy of saturated steam at 350^oC is 2418.3 KJ/Kg

Q = mass x | U_outlet - U_inlet |

Q = 100 (Kg/s) x ( 2418.3 - 2506 ) (KJ/Kg)

Q = - 8770 KJ/s

2)

When the temperature increases at constant pressure, enthalpy of the system increases

The relationship between increase in temperature and increase in enthalpy is

H_P = C_PT_P

where Cp is heat capacity

At constant pressure change in enthalpy can be identified with heat supplied at constant temperature

H_P = q T_P

q =H_P / T_P

enthalpy of saturated steam at 100^oC is 2676.6 KJ/Kg

enthalpy of saturated steam at 350^oC is 2563.9 KJ/Kg

Q = mass x | H_outlet - H_inlet |

Q = 100 (Kg/s) x (2563.9 - 2676.6) (KJ/Kg)

Q = -11270 KJ/s