Question

During a particular the specific heat of the working fluid comprising system is given by the relation: (C=0.2 + 0.002 T) kj/kg K. where T is the absolute temperature in degree Kelvin. What amount of the heat is required to be supplied to the fluid system to raise it's temperature from 300 K to 400K? Also determine the me mean value of specific heat.

Answer 1

The heat is

$$Q=m\int^{T_2}_{T_1}C\text dT=m\int^{T_2}_{T_1}(0.2+0.002T)\text dT,\\\space\\ Q=m\bigg[0.2(T_2-T_1)+0.002\bigg(\frac{T_2^2}2-\frac{T_1^2}2\bigg)\bigg],\\\space\\ Q=180\text{ kJ}.$$

Find mean value of specific heat:

$$Q=cm\Delta T,\\\space\\ c=\frac Q{m\Delta T}=900\text{ J/(kg}·°\text C).$$